Firstly, you are right that it should be pets are, not pets is
Secondly, neither even though nor even when works here. Even though means something like despite the fact. For example:
- Even though (despite the fact) I like pets, I don't want them in my
It does not make sense to write:
- Despite the fact that pets are not my thing, you can always pose with soft toys!
Even when means something like even at the times when (something happens) . For example:
- Even when (even at the times when) my pets chew up my soft toys, I don't scold them.
So this doesn't work either:
- Even at the times when pets are not my thing, you can always pose with soft toys!
The most natural way for your friend to express the idea is:
- If pets are not your thing, you can always pose with soft toys.
- Since pets are not my thing, I (always) pose with soft toys.