There is an old joke in French:
Les islamistes se sont convertis à la démocratie : un homme, un vote, une fois.
The Islamists are converted to democracy: one man, one vote, once.
I first read it in French press coverage of the 1992 Algerian elections. 1st round saw the muslim parties get most of the votes. The 2nd round... never happened as the Algerian military cancelled the vote (launching a bloody civil war).
The French government apparently were convinced to stick with the devil they knew, as they kept on selling dual use equipment to the government (which resulted in terrorist attacks throughout France).
The point is not necessarily that Western countries can't stand "reasonable Islam", it is often that they believe, rightly or wrongly, that elections to put in place certain types of governments tend to see those governments keep themselves in power, by undemocratic means. And become "unreasonable" in the process - certainly a good deal of what's done in the name of Islam is against the teachings of that religion and reprehensible.
Before political Islam, the West had the same concerns about elections putting in place Communist or Socialist governments.
On the one hand, this type of overreaction brought in US support for coups in Chile and possibly Argentina. And the reluctant acceptance of the return of the Egyptian military in power (quite possible the Brotherhood would have cratered in elections).
On the other hand, this fear is not always unwarranted. Iran runs elections, for sure, but to assume them capable of accepting any return to non-theocracy requires quite a bit of gullibility. Ditto the behavior of Chavez and Maduro since getting elected.
One man, one vote, once.
For a while, say 10 or 15 years ago, Turkey's Erdogan was considered capable of bridging that gap and bringing true democracy with a Muslim twist. He's not exactly been shining in that role, although it may be more due to old fashioned strongman rulership than straight out Islamist.
In short, as Arno states, many Western governments prefer a devil you know (dictators) over trusting a country's electorate to manage their affairs sensibly if they do elect a Muslim-oriented government (for the record, I think that is a miscalculation, at least in aggregate).
Last, in the North African/Arabian area, the notion of umma, transcending national borders in favor of religiously-imposed transnationalism isn't exactly popular with everyone. Especially in an unstable region with lots of sadly still relevant oil (and gas!!!).
No doubt, reasons cited by Phillip in his answer do exist and do weigh with Western politicians and electorates. However, not all of us would agree that it is useful and productive to impose Western values on unreceptive societies. I suspect that "not all of us" would encompass quite a few of the old hands in the diplomatic and foreign affairs corps of Western democracies (the realpolitik gang, if you will). They're mostly just concerned with not rocking the boat and not veering in unforeseen, more conflictual (for the West) directions.
After all, to get back to those Egyptian generals, they haven't exactly been promoting women's rights with a vengeance lately, have they? And Saudi Arabia's illiberal tendencies have rarely stood in the way of fairly cordial relations, Khashoggi aside.