It sounds like on her side, she might be concerned that you think that veganism is a religious belief, or you might think that veganism some how disproves the existence of God.
People are strange and believe different things for all sorts of reasons, sometimes for reasons that they themselves don't even understand. Like if it sounds like you are trying to replace belief in God with veganism you might get a cold response (see below)
Exodus 20:3-5King James Version (KJV)
3 Thou shalt have no other gods before me.
4 Thou shalt not make unto thee any graven image, or any likeness of any thing that is in heaven above, or that is in the earth beneath, or that is in the water under the earth.
5 Thou shalt not bow down thyself to them, nor serve them: for I the Lord thy God am a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate me;
As far as the gay marriage issue you mentioned, you never know, maybe she had a gay relationship in her past that she wasn't happy about, or something like that , and isn't open to it for a surprising reason like that. If you decide to go to her church or make her a vegan meal so she can try it out, let us know how it goes, it sounds like it would make for an interesting exchange.
The loin cloth was before they ate from the tree of knowledge. After they ate it they felt shame and had to cover it up. shame and covering up are paralel to each other. What would be the best way to stay true to sinless life in other words godly life?... to live more as god intended us to live before the first sin was commited...
What I was trying to say is that her argument bares no validity if the topic is about sin. The bible is written for people who sin and try to live with less sin. So when debating about religion and lifestyles no one can actually say who is right or wrong... having agro thoughts towards others also counts as 'sin'. ''The tree of knowledge is knowing what is right and wrong. what is wrong is being out of harmony. Everything tends to go back to a chaotic state and harmony is that which keeps the universe together and keeps life in balance. So if you do something which throws the life balance out you are sinning. '' (as said in my awesome mother's words).
You should check out Gary Yourofsky's video on this. He was speaking to a bunch of religious people and he said some thing like :If your God support's (then listed all the horrific things that are happening to animals) , Then what does the devil do?!" So awesome. Check it out: https://www.youtube.com/watch?v=LiZRc71LQQ8
I think it's all up to what people want to take from the bible and how they'll interpret it but I'd say I don't believe God put animals on this earth for us to eat just as woman were not put on this earth to serve man and one race to be enslaved by another.