There are many good and bad poker players - male and female alike. At the "professional" level of poker, the player (regardless of gender) has displayed enough winning attributes to get themselves there. At this higher level of poker skill, I don't think gender in itself would matter in theory. I say "in theory" because every single poker decision along the way is objective. Preflop hand selection: objective. Math for things like pot
odds or
bluffing frequencies: objective. Having an "intuition" about when to fold...objective again because that is based out of subconscious factors that are objective.
Therefore, gender doesn't matter in theory.
Why "in theory" then? I say this because I think that poker is largely (at least right now) about imperfections and not optimal plays from an objective standpoint. 100% objective play would look like two computers playing GTO at Nash Equilibrium in a Heads-up Match. However, human players don't play this way. Even Phil Ivey claims to have never played a "perfect session" of poker due to always spots he re-considers about trying this or that.
In practical play, I do think there is a difference between how genders play poker. However, this is only because the male versus female mind tends to reason differently. This isn't to get arrogant and claim one is superior than the other, but there is clearly a different mindset that each gender typically holds.
As with many things in poker, we can make superficial assumptions that are generally true as long as we are willing to change that perspective in the face of evidence. If someone comes over to the poker table (male or female) and gives me the impression that they are a fish, then I'll "chalk them up" as a fish until they demonstrate otherwise. I am not claiming 100% of the time they are a fish; surely, I can change my perception based on evidence, but there is nothing wrong with recognizing that enough of the time, my assumption that they are a fish is profitable.
Same thing here with gender I think. Assuming a man will play poker like a man and a woman playing poker like a woman is so blatantly obvious, but we seldom think of it that way. take bluffing for example...
It is my opinion (again, I may change freely in opinion in the face of contrary evidence) that women tend to "stick to their story" with a
bluff longer than men tend to do. Stereotypically, men might play poker more aggressively, but I think they are also quicker to back down and hit the brakes if someone plays back at them. I think a woman will typically be more unflinching and stick with the represented story in the hand. Not saying this is always true, but little things like this are not the same in frequency between men and women poker players - so we can't rightfully call them identical.
I would be remiss to not highlight enough that these are generalizations based on observable frequencies that tend to come up. Obviously, this isn't going to be true for every case.