Where did one argue “publicly” in the1950s?
Short answer: media, the press, dedicated organizations for public engagement
Long answer:
Michael Warner has done writing about the place of 'publics' in our society, German philosopher Jürger Habermas etc. Warner is a contemporary writer and Habermas is actually still alive (aged 91) and has argued against Postmodernism and the philosophies that have given momentum to the politics of liberation.
The idea is that 'publics' are distinct audiences ... bubbles with shared interests, who have some amount influence on power, even if that is small. I'm only an amateur who comes to this topic through my interest in McLuhan and Philosophy so I can't do it justice, so please pursue these writers yourself.
The general idea is that " the growth in newspapers, journals, reading clubs, Masonic lodges, and coffeehouses in 18th-century Europe" created the first body of public criticism to question power, and officially sanctioned or tolerated. So when the American experiment was designed, freedoms of association, expression and the press were enshrined in their foundational document. Publics are the foundation for democracy.
Eventually mass media arrived, and was added to the list of platforms considered as 'public' dialogue - but eventually restrictions were added to counteract their special attributes for propaganda. We are essentially still in this period, with the computer and internet media now being as 'public' forums. We're in a post McLuhan period, which hopefully means people are more aware that our media are colouring at least, or actually being the message.
So what does it mean to the topic of identity politics and rights ?
We have a democratic system that was designed at a time when the designers did not consider non-white, non-Christian, non-male landowners to be full citizens... which written even before the mechanical age had started or the age of modern newspapers... They did know that their Constitution had to include a renewal formula, which meant that who was to be considered to be a "full" person would change. Most enlightened framer of the constitution would be considered to be a regressive thinker, by today's moral standard. And yet they created an enduring system that would come to recognize equality of millions.
Now as equality progresses, there are periods of debate wherein we discuss, say, rights for minorities. At such times, such as today, an opinion which is widely held can decline in popularity as a rights debate plays out. So some opinions can thereby become unfashionable, or even repugnant to many . In recent years, there was widespread opposition to gay marriage which somehow evaporated quickly. Barack Obama opposed gay marriage during part of his term as president.
So 'trans women are women' 'trans men are men' have made a foothold in law now. I support the idea, but I also expect that this is a difficult concept for many to adopt so my work as an ally includes helping work through the debate.
The main finding I have from my talks on here is that the entrenched positions won't be resolved, and that one sign of being entrenched seems to be that you can't accept the opposite view being reasonable at all. Like abortion, this is a values debate, and there is actually no correct answer.