Well, one can deal with wireheading by declaring that wireheads don't count towards utility and/or have negative utility.

One can deal with any counterexample by declaring that it "doesn't count". That does not make it not count. Wireheads, by definition, experience huge utility. That is what the word means, in discussions of utilitarianism.

That approach doesn't work in this case since we don't want to assign negative utility to the state of two people being attracted to each other.

We might very well want to assign negative utility to the process whereby that happened, for the same reasons as for forcible wireheading.

I doubt if you intended your comment as an argument against utilitarianism, but rather as an argument for PUA. Am I reading the tea-leaves correctly here?

Why can't I do both?

That is just a way of not saying what you do. Do, you, in fact, do both, and how much of each?

After all, the correct Bayesian response to discovering that two ideas seem to contradict is decrease one's confidence in both.

The correct rational response is to resolve the contradiction, not to ignore it and utter platitudes about the truth lying between extremes. Dressing the latter up in rationalist jargon does not change that.