All males have lower pitch voices, and all females have higher pitch ones? If not then it's not objective.
Actually, it is, when you're not talking about general population employment, but about the best 1 in ten million -- or sometimes even best 1 in a billion -- in some particular aspect. Which really is what competitions are about. Regardless of whether it's sports, singing, whatever.
So, yes, if you're picking some random person off the street, some men run slower than some women. I mean, the guy could be an obese guy with asthma.
But that's not what you compare when you're running, say, an Olympic marathon. Then the men's champion ran it in 2:01:39, with most runners completing it between 2:02 hours and 2:10 hours, while for women it's more like between 2:15 and 2:25, with the world record being 2:14:04. They don't even overlap. The slowest guy (that actually finishes) in an Olympic Marathon will usually be faster than the fastest woman. And not just fastest woman in that competition, but most times it's faster than the fastest woman on record. Ever.
And I'm picking marathons as an example, because that's actually one of the categories where women are the LEAST disfavoured, on account of having some more resistance to muscle fatigue than guys.
The notion that every X must be better than every Y to have an objective difference is simply stonking stupid, idiotic, moronic, knuckle-headed, and a few other synonyms, when what you're comparing is NOT two random people off the street. When you're comparing samples that are already pre-selected to be at the far far right end of the bell curve, then the middle of the curves being offset from each other actually has a HUGE impact on what the chances are to actually find an Y better than an X. Because the chances to find an Y that is even equal to the best X, multiplied by the respective population, might just drop way below 1.
In the case of singers, the notion of a "better" is somewhat less clear, but again there are objective differences. Not just the pitch, which was already mentioned, but also timbre. Take it from someone who actually was trying to pass for a girl at some point, it's a lot harder to pull something that even remotely sounds like a feminine voice as a guy after puberty, than just deciding to use a different pronoun.
Furthermore, for better or worse, both appeal to different demographics, and looks are also a part of it. If you think that <insert random boy band> and <insert random girl band> even compete for the same demographic, you might well be mistaken. So deciding which is best isn't even apples to oranges, it's apples to golf balls.