Sadly, this is not always the case. While the excessive and highly stereotype-driven gatekeeping of the past was a problem, the informed-consent model of treatment has opened a number of very problematic doors, and plenty of people are walking through.
How is that male privilege? I believe firmly in the existence of male privilege, but I fail to see how it applies here, unless you believe that FtM transsexuals get preferential treatment (they don't).