Joseph- while some of that post was very informative it didn’t address the question, which specifically discusses cousins.
You say or quote things like “even between strangers.”
The question was not about strangers, or whether men and women should have platonic friendships. I don’t think anyone would disagree with what’s been said about that. The question was specifically about cousins, i.e., family, and that is not addressed in anything you’ve posted.
Anyway, my two cents is that it depends on the specific closeness of the families in general. If the cousins grew up spending lots of time together, and their relationship is similar to that of brother and sister, than for the same reasons that brothers and sisters can talk, I’d say its permissible. If their relationship is more distant, i.e., they didn’t see each other growing up very often, didn’t see each other except for the occasional and infrequent simcha, then no, they are more akin to strangers who should not develop a platonic relationship. But I am Just-a-guy, not a Rav, and not even Joseph.