The word itself is from Greek then spread to Latin, then split into the Romance languages, etc...

It's "Egoistiko" in Greek but somehow in Latin they always messes up the gender forms and changes them according to Latin, then when it came down to the Romance languages, the also decided to take a different route and yet change the word forms again according to those rules or the exception to those rules or any new rules being made. So someone who knows a little Greek [but no Spanish] will tend to think "egoísto" is correct.

Words like egoista, artista, periodista, etc. are the same for either gender. There is no such word as egoisto.

no, this word hasn't got gender you can only say agoísta, anyway a person who is "egoísta" is a person who isn't generous, (it's so difficult say how is him) xD

You must say egoísta.

No matter if is a men or a women.

Hope it helped