This is ridiculous. "Everyone should get a vote" explicitly rejects the idea that all opinions are equal, as it explicitly rejects the opinion that "not everyone should get a vote".
It is impossible for both of the things you suggest to be true at the same time.
But if “well, women getting to vote isn’t inherently better” is a hill you want to die on…
Are some ideas worth more than others should some people's votes count more than others? You can't have both.