I was wondering about that as well. I also didn’t think that R’ Yehuda HaChassid wrote about cousins.
I can’t say for sure since he has a long list and I haven’t memorized it, but I certainly have never heard anyone say that they are opposed to marrying cousins for that reason, even though I have often heard people say that they won’t do other things because of his takanos.
There are a lot of people who refrain from marrying first cousins, but the reasons I generally hear are either genetic or weirdnes (and in at least one case this was from someone who is makpid on some of the takanos of R’ Yehuda HaChassid, yet didn’t mention it as a reason not to marry a first cousin).