I looked at your profile and saw that you're an American.
You are confused by Bob because you assume that the political positions held by the Democratic Party and the Republican Party are directly analogous to what "Leftists" and "Rightists" should or do actually think. This is not the case. The parties in the United States effectively act as standing coalitions of broad swaths of people with different interests, and as a result adopt positions that don't actually make coherent sense when assessed for intellectual consistency.
Let's look at Bob's opinions in detail to illustrate this a bit.
Bob is in favor of social safety nets and LGBTQ rights (Leftist).
As a matter of pure ideology, there is no intellectual reason at all for LGBTQ rights to be considered leftist, or in any way related to social safety nets. Many leftist governments around the world are notorious for treating LGBTQ people poorly; the most prominent example I can think of is Cuba, which until recently used to imprison people for life if they had AIDS.
So why are they in the "leftist" coalition in the United States? The answer is because social conservatives interested in traditional marriage are in the Republican party (which is arbitrary and discussed later), and it's somewhat contradictory to have a party that favors the supremacy of traditional marriage and LGBTQ rights at the same time. So, the LGBTQ rights people end up in the Democratic party by default.
Bob is also very pro-capitalism and in favor of gun rights (Rightist).
What do gun rights have to do with capitalism? Like the other example, these are issues that are not directly related to each other; the United Kingdom is a country that is capitalist and has very prominent advocates for more capitalism rather than less, yet the idea of gun rights becoming a movement there seems like a long shot.
This association is another product of the two party system. During the Cold War, groups of people with different political interests found it mutually beneficial to form a political coalition, namely free-market types, social conservatives, and anti-communists. The resulting "fusion" became the conservatism that found a home in the Republican party and was its governing ideology until 2015 (or arguably as earlier). The main thing that held these people together was a commitment interpreting the constitution as a document that generally restricts government power (at least domestically), so, when the modern gun rights movement started taking off in response to the Gun Control Act of 1968, the Republican party just happened to be the natural place for people with these interests to go.
So... your confusion about Bob is really because you equate the hodge podge of political party positions, which are the product of coalition building and thus are not always consistent, with larger ideologies that tend to be normative and therefore should be consistent. But... you came here looking for help, asking a particular question; maybe now we can answer it:
This is difficult to explain to people when they ask, so is there an easy-to-grok term for this? I actually encounter people like Bob reasonably often.
This is hard to give an accurate answer to because we don't actually know how Bob arrived at his opinions, we just know they don't perfectly line up with the Democrats or the GOP. So I make the following recommendations:
Ask Bob what he calls himself. If you are already talking to Bob about politics this much, it shouldn't be a rude question. Bob may have a specific identity that would explain his seemingly contradictory viewpoints as actually being the product of a consistent ideology you haven't heard of before, and he might be willing to share that with you (I'd bet if that's the case, he's probably a libertarian, but I wouldn't go around assuming that without more evidence).
If Bob's opinions really are picked randomly, or if you do not find out how he arrived at them, I would describe him as "politically unaffiliated", "non-partisan", or, if it's not the
name of a party in your state, "independent." That conveys that he's not really a Democrat or a Republican, but it doesn't make him sound like he has opinions in the mushy middle the way that "centrist" or "moderate" does.