Sometimes yes, sometimes no.

Even if playing with a fixed-pitch instrument, it only really sounds out of tune if they're playing the same notes. Which in the styles I play isn't an issue.

So I guess how often this happens in practice varies between styles and eras of music, which would make sense to me. I haven't ever done early music and know nothing about it (other than trombones used to be designed terribly and we now know how to make better ones ;)

Source: Also have a postgrad in music, probably from one of the conservatories your spouse teaches at, and still play trombone professionally.