Not really adding much but as the person who put it on feminist bingo I feel compelled to reply.
Firstly a humanist is totally different. Humanism is in opposition to religion so I don't see them as connected. People can happily be both but I don't see a particular relationship.
On equalist:
It is usually used by people who are feminists in that they express feminist beliefs, but then use the term equalist to say they are something different. Doing this takes away some of the meaning of feminist. It takes feminist principles, but labels them as something other, which then reduces the meaning of feminism to not include these things. So it works in favour of those trying to perpetuate myths about feminism by removing the bits that people do accept. It then others the feminist as something different to this, and therefore less palatable.
It denies the heritage of a movement that people fought and died for. Equalism doesn't have this.
It removes the dimension of inequality from inequality. Women are the ones suffering from inequality. They are the ones who need to have their position changed to become equal. Equalism hides this and suggests that inequality isn't sex driven.
It is also usually used to attack feminism, and to imply that feminist aren't interested in equality.
I get why people are attracted to it at first. But those are the reasons I object to its use.