Gatekeeping is a term that describes those who take it upon theirselves to decide who does or does not meet the criteria of identifying as LGBT. This term is often used in regards to transitioning, where there are strict formal requirements one must fulfill in order to transition medically or legally. However, it can also be used to describe exclusion of transgender people from gendered spaces (such as public bathrooms) by demanding that they "prove" their gender identity against an arbitrary standard before being allowed to enter.
The term "gatekeeping" originates from the medieval idea of a guard on a gate into a secure place (such as a castle or walled town) who is required to check anyone entering in order to ensure they are not spies, impostors, or a threat to the security of the area.
Gatekeeping is often seen as a form of transphobia because it holds transgender people to higher standards than cisgender people by believing trans people's gender identity is less valid.