there can be conflicts between the two, for sure: full censorship resistance means that even the author can't delete posts anymore, while privacy is based on forgetting information or not storing it in the first place
but i don't think it can sensibly be extrapolated to a general law "more censorship resistant means less private"
that's like saying "staying silent and not expressing yourself is the best privacy solution"
and they often go together: making it impossible for the government to read your messages also makes it impossible to selectively censor them