What's the difference?

The latter removes any scope for taking circumstances/details into account which is an issue irrespective of gender/age etc (e.g. "believe men" or "believe children" would be equally absurd).

But you just said "believe women" is fine whereas "believe men" or "believe children" is absurd. I don't follow the distinction you're drawing here. They're grammatically equal.

I am saying blanket "believe <anything>" is absurd and I do see your point; there isn't much difference.