There's a clear connection between Nazism & anti-abortion, anti-gay conservatism

Nastiness. The clear connection, at its heart, it's nastiness. Lack of compassion. Zero empathy.

If you are not Aryan you can be sterilized WO any problem.

It’s almost like both the Nazis and the queers have been saying that

May 6th, 1933, Date of the first Nazi book burnings. The location, Berlin Institute of Sex Research.

Is a tree connected to its leaves?

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.

See? They Owned the Libs!!!