Summary of answer:
- A poll that would satisfy the conditions for this question is unlikely to exist, given the common negative (and sometimes inaccurate) associations of the term "incest" or "incestuous."
- The standard arguments made to differentiate incestuous unions from gay unions are discussed in many media sources that have covered the gay marriage debate, including, for example, here and here. (For a summary of points from these links, see the bulleted list below.)
For a more detailed consideration of the questions, read on.
For the first question, I seriously doubt you're going to find any polls asking people whether they are in favor of incest. From a brief search, I couldn't (though there are some polls asking people if they have been the victims of incest or know of incestuous abuse). For most people, the term "incest" generally conjures up images of abuse, often father-daughter relationships (or father with minor child in general), or perhaps brother-sister abusive interactions. I don't think we need to do a poll to see that this is the common association of the term (at least in the U.S.); just look at its usage in any news story or really most of the time it comes up.
Obviously, consensual incestuous relationships are theoretically possible and probably do happen in a minority of cases. But it's unlikely that the vast majority of people would ever say they are "in favor of incest" in a poll, because it is generally taken to be synonymous with abusive incest. In a way, it's not unlike the associations that homosexuality had decades ago: it was assumed to be deviant, including mostly weird people and child molesters. (To this day, there are many people who maintain that association with homosexuality. They do not see a difference between pedophilia and homosexuality, assuming that someone who practices one is just as likely to practice the other.) Similarly, to many people "polygamy" is equivalent to the idea of a guy abusing young girls and forcing them into marriage. That may be changing slightly with media stories, the series Big Love, etc. Still, the idea that "polygamy" could refer to an adult woman with multiple (consensual) male partners or even three women in a consensual relationship is just not what most people think of when the term "polygamy" comes up. (Again, just look at most news coverage to see these assumptions and associations.)
Because of these associations with incest, you're probably not going to find a poll. And if you did, it would be meaningless anyway to answer your question unless the pollsters took time to explain to those polled what consensual incest might actually mean and convince people that such things might exist.
I also think, in the absence of polls, that you can look at the way incestuous relationships tend to be portrayed in the media and in the courts, even among liberals. The case of Patrick Stübing, who has had a consensual incestuous relationship with his sister for many years, shows that a country with liberal marriage laws (gay partnerships have been legal in Germany since 2001) still will put someone in jail for consensual incest. The European Court of Human Rights also upheld that conviction, again despite having many member nations that approve of gay marriage and/or gay partnerships. A similar prosecution happened to Columbia professor David Epstein, who had an apparently consensual sexual relationship with his adult daughter. In that case, most gay marriage advocates in the press found themselves coming up with all sorts of reasons why incest is different.
And that leads us to the second question: clearly most people who write for the media in favor of gay marriage tend NOT to be in favor of incestuous marriage. All one needs to do is scan the news for any point in the past decade when any major public figure has associated the two, and you'll see days of coverage afterward while that person is denounced by those in favor of gay marriage. I have no idea what the general public might think, but clearly the public voices of the gay marriage movement react in strong negative association to ANY comparison to incest.
Since you ask for specific examples of arguments public figures tend to use to differentiate the two, here's a detailed article (which covers polygamy, incest, and bestiality). The David Epstein article linked above also contains a lot of the standard arguments.
In sum, here are the standard arguments, which you can read about in more detail in the links:
- Genetics (obviously not applicable to homosexual incest)
- Exploitation/abuse (discussed above)
- Disruption of family dynamics: as the German court ruled: "Incestuous connections lead to an overlap of family relationships and social roles and thus to a disturbance of a family bereft of [clear] assignments. … Children of an incestuous relationship have great difficulty finding their place in the family structure and building relationships of trust with their next caregivers. The vital function of the family for the human community … is crucially disturbed if its ordered structure is shaken by incestuous relations."
- The "Many Other Possible Partners Theory": essentially, the idea here is that people have other choices to form relationships outside of their family. A homosexual who is banned from homosexual relationships has no possibility for a relationship, while people in incestuous relationships could still have many other opportunities for relationships outside their family unit.
The last two of these are the ones that typically come up when incest is discussed beyond the possibility of abusive incest. Here's an extended explanation from the Epstein article linked above:
When a young man falls in love with another man, no family is
destroyed. Homosexuality is largely immutable, as the chronic failure
of "ex-gay" ministries attests. So if you forbid sex between these two
men, neither of them is likely to form a happy, faithful heterosexual
family. The best way to help them form a stable family is to encourage
them to marry each other.
Incest spectacularly flunks this test. By definition, it occurs within
an already existing family. So it offers no benefit in terms of family
formation. On the contrary, it injects a notoriously incendiary
dynamic—sexual tension—into the mix. Think of all the opposite-sex
friendships you and your friends have cumulatively destroyed by
"crossing the line." Now imagine doing that to your family. That's
what incest does. Don't take my word for it. Read The Kiss. Or the sad
threads on pro-incest message boards. Or what Woody Allen's son says
about his dad: "He's my father married to my sister. That makes me his
son and his brother-in-law. That is such a moral transgression. I
cannot see him. I cannot have a relationship with my father …"
Homosexuality is an orientation. Incest isn't. If the law bans gay
sex, a lesbian can't have a sex life. But if you're hot for your
sister, and the law says you can't sleep with her, you have billions
of other options. Get out of your house, for God's sake. You'll find
somebody to love without incinerating your family. And don't tell me
you're just adding a second kind of love to your relationship. That's
like adding a second kind of life to your body. When a second kind of
life grows in your body, we call it cancer. That's what incest is:
cancer of the family.
These are the general sentiments that usually comes up in the media when your question is asked. One can obviously question the logic of these arguments. For example: Don't all marriages have power dynamics, many of them unhealthy? These unhealthy power dynamics might in fact have something to do with the fact that until recent decades, women were generally an oppressed class. If we're going to outlaw marriages that result in screwed up relationships with messed up power dynamics, we might have to cast the net pretty wide.
And as for the "just find another partner outside your family" argument, is that argument applicable when we're talking about a fundamental right (as marriage is generally characterized in the gay marriage debate)? Should you lose your right to marry someone just because there's a social stigma, and "there's lots of other fish in the sea"?
(From a purely legal standpoint, actual marriage brings up other practical problems about inheritance and other marriage benefits. Particularly if you allow intergenerational incest, you would end up messing up a lot of the legal apparatus that deals with marriage vs. heirs/relatives.)
There are lots of arguments out there. But it's pretty clear from even a few cursory searches that the common view among gay marriage advocates is that incest is different -- among the media anyway, and probably on the internet in general, if comments on forums are any indication. Whether or not you find arguments on either side convincing usually seems to be based on how you "stack the deck" from the outset.
For example, in the question, it is already presumed that there must be an obvious "rational argument" against intergenerational incest. To many other people, there are obvious "rational arguments" against all incest, against gay marriage, against interracial marriage, against just about anything. What is "rational" depends fundamentally on what assumptions you begin with. I think it's undeniable that it is possible for an intergenerational incestuous relationship to be consensual (and perhaps even have a power dynamic that is very different from what you would assume). I also think it's undeniable that the vast majority of incestuous relationships among close relatives (not talking cousins here: fathers/mothers with sons/daughters, siblings, aunts/uncles, etc.) tend to be psychologically damaging, if not outright abusive.
In the end, the question comes down to how much freedom you're willing to grant vs. how bad you think the chances of abuse are (for whatever sort of relationship you want to allow). Obviously abuse is illegal in all relationships, but the main concern among most people is probably that legal incest would encourage more abusive relationships. Since there haven't been a lot of countries experimenting with legalization of incestuous marriages, we don't have any data on what effect legalization might have. So, "rational arguments" usually tend to just be about what you're personally comfortable with.