As far as I can tell, your intended meaning is absolutely correct, but you have some of the terminology wrong: fascism is an explicitly right wing form of oppressive authoritarianism. The extreme left can be authoritarian and oppressive, but never fascist.

Stalinism and the ideology of Pol Pot and his Khmer Rouge are notorious examples of tankies: left wing fanatics who engage in oppressive authoritarianism and violent persecution of anyone different from their narrow definition of the ideal citizen, often using arbitrary metrics just like fascists do.

Is the end result the same for an LGBTQ+ person, a pacifist or anyone else demonised by all forms of oppressive authoritarianism? Yes.

But that does not make the ideologies identical and the distinction is important because the differences mean that different tools are more effective in combating one than the other.