Is it possible to create a performance review system that somebody won't complain is sexist?
In turn, giving up on building a less sexist system because people will always complain is like giving up on building a more secure infrastructure because people will always complain.
Unless you are extraordinarily lucky at both the humans building what you're building and the inputs to your system (constraints about language and tech stack and problem domain on the security side; constraints about hiring sources and existing culture/public reputation and leadership on the employment side), you're always going to have security flaws in your infrastructure, and you're always going to have sexism in your employment processes. And even if you are this lucky, you're not going to eliminate people poking at your system and suggesting places where it seems to fall short. The important question is what you do about it, how severe the problems are now, and how the severity changes over time.
Just like there are plenty of ways to write software that take it as a given that implementors will screw up and attackers will be clever, there are also plenty of ways to design a performance review system that takes it as a given that some fraction of humans in your organization will have biases (conscious and unconscious) and will treat their coworkers according to their biases.
Honestly, some of the mitigations are the same: the first thing I'd reach for is defense-in-depth and auditing. If your system is consistently giving different results (whether it's hiring, or retention, or promotions, or salary) to people in different demographic groups in a way that seems to disprove the null hypothesis that the demographic is irrelevant to job performance, look very hard at it, add additional reviews to make sure the results are consistent even when different people are involved, and keep measuring. There might be good reasons that the disparity is legitimate (just like there might be good reasons that one of your servers is regularly opening outbound TCP connections to random machines in China), just make sure you are actually noticing that something unexpected is going on and try to find an explanation for it.