Should I ignore the vendor directory in git for Drupal 8?
There isn't really a right or wrong answer, it will come down to your situation. Composer themselves have pretty strong feelings that yes, you should ignore it, and in an ideal world that's definitely what you should do, but it's not always that straightforward.

It depends mainly on your hosting and deployment process. If, for example, you're on Pantheon, and don't wish to implement a complicated upstream workflow, involving a dialogue with their technical staff, you're forced to commit all dependencies to the repo. There's no Composer sitting at the other end waiting to run when your code is pushed, if you don't push those files up yourself, they're not there, and things will break.

Similarly if you're on shared hosting and don't have a CI workflow, you're probably going to be forced into lugging all the files around with you in one way or another.

Basically if it fits into your development/deployment workflow to be able to exclude those files, it's a good idea to (for the reasons listed in the link above).

If it doesn't, committing them to the repo is absolutely fine.