Sex is so deeply ingrained in humanity - heck, not just humanity but mammals and animals writ large - that it is almost certainly impossible to create a world where people genuinely treat trans people the same as cis people. Sure, outlawing discrimination in housing and employment against trans people is not only feasible it's been implemented in most liberal democracies. But that's just the tip of the iceberg when it comes to the difference between living life as a trans person versus a cis person. Gender is a social construct. Sex is biology. For many people, the latter is more salient than the former.
This is why talking about what the outcomes would be in some hypothetical world is pointless. Doctors are striving to deliver the best outcomes in the real world, not the outcomes in some hypothetical world that doesn't actually exist and probably never will.
> yet also use the discrimination against trans people as a justification to discriminate against children exploring gender, i.e. trans children.
Children are free to explore their gender. Just not with powerful drugs that have lifelong effects. Refusing to prescribe puberty blockers to a child experiencing gender dysphoria isn't discrimination any more than it is to refuse to prescribe artificial testosterone to a boy that has normal levels of testosterone for his age. We "discriminate" against this boy that wants to explore hypermasculinity, too.
> I wonder if we existed in a world where soft boys were beaten into becoming less emotional, who grow up to be unemotional men. In a society where adult men are beaten if they express softness, are these men considered happily unemotional? How would we be able to tell?
You would measure their health outcomes: do the latter experience depression or other negative mental health conditions at different rates? Do they die by suicide at different rates? I haven't dug deeply into the effects of corporal punishment, but presumably it's discouraged because we've observed negative outcomes.
> How do we tell if someone is cis when it is stigmatized to be trans or express gender dysphoria? Genuinely not sure, honestly.
I'm not sure what you mean by "how do we tell if someone is cis". I think you mean something along the lines of "how do we tell which gender dysphoric children will or won't continue to experience dysphoria in their cis gender past natal puberty?" If that's the case then the answer is "we can't". Psychologists tried, for decades, and failed to predict the minority of patients that would persist in cross sex gender identity. We know that ~80% become comfortable in their cis gender after natural puberty. This is why it's hard to justify prescribing puberty blockers. Suppressing natal puberty will help someone pass better in a cross-sex gender, but the benefits of passing better need to be weighted against the probability that the child would live comfortably in their cis gender without dysphoria absent blockers.
Which is the better health outcome? 5 trans people who medically transitioned before puberty, or 4 cis people who live comfortably without dysphoria in their cis gender and 1 trans person who transitioned after natal puberty? Ideally we'd be able to predict the 1 patient that would persist, and transition them medically before puberty. But again, we don't have that ability. Thus, it's insufficient to justify prescription of puberty blockers by pointing to the one trans person who medically transitioned as an adult and say that they would have had a better live if they were able to transition medically before puberty. This is the big reason why advocates for puberty blockers tend to dislike discussion of persistent rates with versus without puberty blockers. It's fairly easy to justify them in the simplistic world where all gender dysphoric youth are guaranteed to persist. But factor in the persistence rates without blockers and it becomes vastly harder to make the case for them.