Like, the largest demographic of victims were Jewish, but there was a bunch of other groups getting the same treatment.
The difference is LGBTQ was hated by both sides. After Alan Turing contributed more to stopping the nazis than probably any other single person, England chemically castrated him due to his sexual preference which likely contributed to his suicide.
Fascists always prioritize the easiest targets first
Not exactly, Nazies take on many forms. American Nazies want more slaves. Minorities need to have more babies... as long as they stay poor and uneducated.
Don't say Nazism when you mean: racism, authoritarianism, totalitarianism, discrimination, etc. They are often overlapping, and components of each other, but not the same thing
I would argue that the connection is a lot older than Nazis. The era around 1250 responded to a nasty wave of the Black death by Christian leaders collaborating to simultaneously fight the population decline by criminalizing abortion friendly midwifery and ostracize and subjugate gender and sexual minorities because they feared the collapse of society due to a population bust. As such what was taught by the church up to that point began to get new connotations. Jewish populations were persecuted and killed as scapegoats for the cause of the plague. Folk medicine women and non-conforming men were killed and condemned for witchcraft. While women stepped up to fill the roles of men during the plague once the population was rebounding their power of place in society was to be broken as the Church leaned on it's misogynistic practices and preached of the dangers to society and the family...
Nazisim is just a more modern echo of well established means to break the power of non compliant of groups who can be scapegoated or subjugated into subservience to Christians who feel threatened, a group that centers nominally celebate and wealthy men whose only contact with women is in a subordinate role.