The "believe [all] women" isn't the women part, but the believe.

Believe means "accept without proof". But the story behind it is "take women seriously, don't dismiss them outright".

By design or by bad luck those two understandings clash. More importantly they clash along ideological lines.

This leads to uneccessary conflict radically slowing down progress. And this benefits all established political forces - the more energy and time everyone expands on this, more elections can be won without being forced to do anything about other topics.

This is not the only feminist/left slogan with the same problem and the same result: agresive pushback.

So, my suggestion would be: don't change definitions of words when designing slogans.

In this case: "take women seriously"