but stop at equality for everyone, not suppression of those you may disagree with
Equality for everyone requires the suppression of those who would take away that equality, otherwise you eventually lose equality for everyone. This is similar to how maximizing freedom for everyone requires restricting your individual freedom to harm others, because in doing so you remove their freedoms. Your individual freedom is less, but the total amount of freedom in the system is greater for it.
Furthermore, it is not a moral failing, or even a difficult moral quandary, to suppress people for their actions and choices. We do it all the time to murderers and other criminals, or even people who don’t shower. This can be done in multiple ways, including ways that do not involve state power. We frequently use social means to suppress people, for good or bad. A society simply works that way. And if they don’t like it, they can simply choose to stop trying to take away equality; I cannot similarly choose to stop being the kind of person they want to take equality away from.
To protect equality we must win every fight; to lose it, they need only win once. Everybody is protected by equality so long as they believe in it. I do not believe that those who do not believe in equality should be extended its benefits, for they will seek to destroy it from within like a parasite.