No disrespect intended, but it feels nothing like a religion to me. And in fact more of a polar opposite.
Veganism is a choice made out from logic and empathy.
We know that other animals suffer, have emotions and feelings.
It's a simple case of extending our circle of altruism to include all sentient life. We wouldn't hurt our neighbour or our dogs and cats so logically it follows we shouldn't do that to other animals.
Religion on the other hand is a set of rules , often laid down by people with a very much less detailed understanding of nature and the world around us, and usually with a completely different outlook on life.
Religious doctrines don't change, although people conveniently pick and choose which messages they think must be followed and which they can abandon as being either allegorical or simply fit for the times they were written.
Religion often leads to people treating other people (and other animals) worse, not better as it engenders a tribe mentality of us vs them.
There is a distinct lack of logic and often a lack of empathy.
Religion has been a major cause of wars and atrocities in the name of xxxxx.
Try being a Christian in Somalia, or a Sunni Muslim in Iran or Baha'i in Yemen.
So no, not really.
Veganism is like a religion in about the same way as football fans are like stamp collectors... i.e. Yes, it's a way of grouping people and they form communities, but that's about it.
I am extremely happy it makes you happy, but I loathe any comparison with religion.