Gyms can install a separate 3rd space changing room for transgender clients, which would allow their participation without excluding the women who want to use the gym.
Women should not sacrifice their privacy, safety, dignity and right to single sex spaces in order to appease a tiny minority. Allowing all men free access to female changing rooms on demand, as long as they claim to identify as women, is a flashers’ and voyeurs charter. And which teenage boy wouldn’t claim to be trans, if it gets him in to see naked women?