Most people think the word Faggot means a gay person, when that is not true. A faggot can also mean a person who is widely generally disliked, for one reason or another. The word has evolved into a more contextual word.
Anyways, here is what Faggotry means:
If the word Faggot is more contextual, so is the word Faggotry
Example: If a person is called a faggot because they are stuck up, or believe they are better than other people, the word faggotry may mean that they are in the act of verbally expressing how they are better than other people than they really are.
Kevin: Im better than you guys at like, everything...
Jonathan: *to Jimmy* Oh, watch out, their is some major faggotry going on over here
Jimmy: Yep. Affirmative. Level 9 faggotry going on over here.