I don't think this is a good strategy to take in a compassionate society, and I think to the extent that we're not living in one, fixing the lack of compassion through understanding etc. is the best approach.

The problem is that it is normal to be abnormal in some way because "normal" does just mean "typical", and we all have so many different aspects to ourselves that it would be quite surprising if most of us weren't weird or special in some way.

The idea that it's fine to be cruel to people simply because they "aren't normal" is the problem. Being not-that-normal is fine; it's the cruelty that isn't.

Red hair isn't normal. (Seriously, statistically, worldwide, it's not.) Let's bully redheads!

It isn't normal for women to be colorblind. Let's bully colorblind women!

It isn't normal for men to be under 4'10" tall. Let's bully men with dwarfism!

It isn't normal for people to have six fingers. Let's bully people with polydactyly!

If we reject every such attitude and instead accept that, yes, people can be unusual in some ways and that's fine, and we can even make accommodations for such people like indicators that use multiple modalities to convey information and step-stools and so on, then there's little argument not to extend the same graciousness to trans people as well.

That seems better to me than how the status quo is turning out, and doesn't hinge upon arguments about the definition of what constitutes normal, and "you can't to a high degree of certainty conclude X so therefore you have to act as if not-X". It hinges instead upon being decent human beings.

That's all that's needed to get the "normal laws" that you say are all that you ask for. If you ask for more, well, it won't necessarily go that far; and the precise details of the normal laws needn't necessarily be exactly as you envision. But to just be supported in the everyday ways that humans need to be supported, it's enough.