And here we were having a very nice discussion without pointing out any potentially controversial/mindkilling examples. Using the phrasing of second and third wave doesn't make it less subtle or less potentially mindkilling.

In the specific case which you are not so obliquely referencing, there's a pretty strong argument that much of thirdwave feminism has strands from first and second wave, while also agreeing on the most basic premises.

It is also worth noting in this context, that movements (wherever they are politically) aren't in general after rational discussion or true beliefs but at accomplishing specific goal sets. You will in any diverse movement find some strains that are more or less interested in rational discussion, but criticizing a movement for its failure to embody rationality is not by itself a very useful criticism.