Maybe a more appropriate term would have been "pedantic" instead of strict, to avoid the miscommunication? I think I understand what you mean. I am nor racist nor transphobic nor <insert-minority>-phobic (at least I hope so), yet I think that the debate about, for example, biologically male people in female sport competitions ought to be (whatever my opinion on the matter might be) and that alone could flag me as transphobic to some people. But I'm not sure they are more "strict anti-transphobe", I just think they are more pedantic, that's all.

Anyway, in the end of the day it was clearly a miscommunication, not necessarily a divergence of opinion. Words are hard.