I'd have more respect if a biological male had applied who presented as a male, and who said that they felt that they had the right skills to be the CEO and explained why, and also agreed that access for women to biological women counsellors would be protected. If he then also argued that there should be services for transwomen, and also for males who present as males, and that the centre should expand to provide this (or other centres should be set up), then I would listen and consider their arguments.
But by totally ignoring the fact that the job was for a woman, and ignoring why this was, and knowing that they were not one, but still tried to get the job - it feels deceptive and like they have no understanding of the needs of women. And how they can square that with being a CEO of a rape crisis centre, I don't know.
It's a completely separate issue from whether rape crisis services need to be provided to trans people, and to men, and what the best ways to go about providing those services are. You don't get that by hiring a transwoman for a job that was intended to be for women, to run a service that was meant to be for women, because that will just mean that that particular service then becomes for transwomen instead, and biological women won't all be comfortable using it.