Presuming that a female ref has been given a premier league game on merit rather than due to identity politics, the major relevance of gender as far as I can tell is in how the players react to the ref. In years gone by one of the unwritten allowances was that big club players could crowd around a ref and bully them. Think Keane and his lot at United, or Terry and his lot at Chelsea. I always thought that they might be less likely to do that to a woman, or at least that they might finally get properly called out for it if they did.
Nowadays players don't seem to crowd around refs so much. I think that is partly because they are soulless robots, and partly because they know the ref isn't responsible for the big decisions anymore, its some guy in a cubicle in Stockley Park, so what's the point?
The idea that a woman ref would be better or more fair than a man just because of gender makes no sense to me at all. The quality of the ref is determined by their ability, which is a good argument for ensuring female officials are given the same opportunity as male ones, but not an argument for promoting female officials per se.
The idea refs are unfair or biased appears, to me at least, simply childish. They make mistakes, that's all. Always have, always will. The key factor is that players almost never play honestly. To take even a small example, every time a ball goes out of play between two players you get appeals from both players for the decision. Every time. We are so used to it that we don't see it. Refereeing is made hard by players. Always has been.
All that has changed is that each and every decision is scrutinized in a way it never has been before (that's down to the dickheads on the telly, and the deflective moaning of losing managers), which in turn has led to the wholly wrong attitude amongst officialdom that every single decision in every single game must be technically correct. They are obsessed with the letter of the law and totally disregard the spirit of the game. We now have offside by a toenail, every contact forensically analysed from ten angles in slow motion, players closing down with hands behind backs, and constant delays and breaks to the speed and flow of the game while someone checks its all technically correct.
Not only does this kill the emotion, it also stops the ref from getting into the spirit of the game and seeing events in context. We used to say that a good ref was one you didn't notice, but now they have to be seen to be everywhere all the time. They can't leave anything to the players to sort out for themselves, which used to be a huge part of the game. Plus, VAR and officiating are all very heavily tilted towards giving fouls and offsides for the slightest thing, with very little disincentive for play acting and exaggerating.
Instead of VAR punishing dishonest play, it just encourages it. Players fall over all the time now because they work in an environment where it makes sense to do that. The telly knobheads never, ever use the word 'cheat', let alone something as archaic and offensive as 'unmanly', both of which would once have been applied to a player going over and holding his face for no reason. The VAR refs are looking at everything ten times to find something to give. Why would anyone play honestly? Players used to take issue directly with a diving opponent, now they just smile at them and accept it, because none of them have a moral leg to stand on themselves. How can anyone ref well when the players cannot be trusted at all, and the tool we could use to address it isn't used that way?
And its not like VAR helps refs equally and consistently. It's not like anyone is saying "Well, I don't like VAR but at least now decisions are always correct and there is no disputes on that front..." Far from it. Instead there is the lingering doubt that VAR will come under far greater pressure if it doesn't get involved in a big game, or that its a random generator. How does that help a ref? I thought the La Croix sending off at Man U was fair enough, but the fact is the ref wasn't going to give a red until VAR got involved. The day before, I watched Bournemouth v Sunderland and saw the Sunderland goalie elbow an opponent in the face (not properly, but enough that you've seen VAR start crying and bleating in other games), a Bournemouth player two-handed push a Sunderland player in the back from behind as he was shooting, sending him sprawling (for once, no need to fake it) and in both cases VAR just shrugged. How can one decision be forensically deconstructed for three minutes, and another skipped over in seconds? If I am the ref, can I keep my whistle quiet and rely on VAR for any key moments, or will it stay silent even when something significant has happened? If I give a decision, will it overrule me? Will I look a dick in that case? Is it better to give nothing, even if you think its a foul, just in case VAR is awake today?
How can anyone, male or female, referee well in that environment?