Good question since the term is a neologism.
Gender: the range of characteristics pertaining to, and differentiating between, masculinity and femininity.
Equal: the same in number, amount, degree, rank, or quality.
-ist: a bound morpheme that means "one who ____"
A Gender Equilist is one who considers gender to be a designation that is is the same in degree, rank, or quality
Its all pretty balanced. But this is not to say that women and men are alike. We are all individuals.
Male and female personalities fall on a continuum in all areas. There may be more males on one end, but there will be some females too. There may be more women at the other end, but there will be males, too. Most are in the middle.
Some males are really pain in the asses, but thankfully, not all. Some females are really pain in the asses, but thankfully not all.
We all need to learn how to be discerning judges of character in order to be safe in this world. However, to use one's image of a group and apply it on an individual level is bigotry and a clear sign of difficulty discerning character.
There is a sticky gender issue: reproduction. Even though it takes two to perform this little miracle, for one gender it is a physical commitment of over a year (with breastfeeding, which is the ideal). We need to be able to work out how our society will respond. Parental responsibility, abortion, birth control, that a baby is "the ticket" to benefits for many girls, parental leave, fetuses identified with anomalies, etc. This spills out onto alternative marriages (I do not understand why the gov is involved in any marriage. The fed involvement should be limited to civil unions at best). Let the individuals work out the details of relationships.
Those who choose to polarize this discussion by posting inflammatory videos and posts are haters (whether its about gender, race, ability, etc). I get really sick of reading the same old shit from these haters.