Anti LGBT folks may actually be gay themselves and hide within these hate groups. Do you know of any names of these groups besides the Nazi party?

It is well documented by social scientists that many who exhibit extreme homophobia do so as a means of reaction to the homosexual feelings they harbor within themselves. It is for this reason that there have been several cases where the founders of anti-gay therapy camps (which are illegal in many countries) have been uncovered as gay themselves, or what they call "ex-gay." These people define homosexuality as "same-sex attraction" and imagine it as a disease which can be cured, which is itself an attack on LGBT people.
Many of the anti-LGBT hate groups active in the United States at the moment would not be considered, by many, to be in the same league as the Nazi Party or other virulent right-wing groups. Indeed, they often masquerade as pro-Christian "support" groups committed to protecting the American way of life. One of the more widely known anti-gay groups is the Westboro Baptist Church, which has picketed the funerals of many gay people and is widely known for its "God Hates F*gs" signs. But other, quieter groups continue to disseminate harmful information about gay people—Focus on the Family, for example, is a good example of a group which pretends to crusade for "family values" while actually peddling a very harmful homophobic agenda.
You can read more about anti-gay hate groups here (also linked below).
https://www.splcenter.org/fighting-hate/intelligence-report/2010/18-anti-gay-groups-and-their-propaganda