@SirChenjins
A few suggestions - no idea if any of these will work!
1.Gay people weren't demanding to be seen as something they are not. The issue here isn't whether trans people should be protected from discrimination and harrassment (no one disagrees with that) - it's how far other people should be required to pretend something that is untrue is actually true.
2.The law does protect those with a genuine conviction that gay marriage is wrong - which is why you can't have a same sex marriage in a Catholic Church, for instance. No such concessions are proposed by trans campaigners - who notoriously don't even think rape centers are allowed to be female only.
You could try pointing out the many logical contradictions in gender identity theory - I actually think we don't do this enough! My own line is "I don't accept GIT because I think it's illogical and even those who say they believe it actually don't - their behaviour and life choices don't match their professed beliefs."
a. If being a "woman" or "man"is nothing to do with being female or male why do trans people need to change their bodies to look more male or female? "Being a woman has nothing to do with being female but in order to be a woman I must look like a female" makes no sense.
b. Words don't exist in a vaccuum - if people say they are a "man" they must have an idea in their head of what a "man" is? What is that other than a male person? Has anyone identified as a "pookahen" or a "tehdyet"? Why not?
c. If you can't define "man" or "woman" these words become essentially meaningless yet trans people claim that it's literally life or death for them to be seen as a "man" or "woman"? How can words be simultaneously absolutely meaningless and completely meaningful?
d. If all the female people in the world suddenly identified as "Ponkens" would it be legitimate to exclude women from Ponken-only sports and services? If not, why not? Do you think that trans women would suddenly start identifying as "ponkens" too?
e. And if you have no answer to these questions then how can you claim someone (your loving mother) is "bigoted" for not accepting gender identity theory? Maybe your loving mother doesn't believe it because she just doesn't think it makes sense!
Good luck!