They may say "come on, we'll go easy, it's not a big deal" but they won't force you or something.
But if they do, or if they give an ultimatum,then those places/trainers suck. If you have valid reason to not spar and they still say "come on" leave the gym because it's not healthy.
Usually the gyms I've been to, they spar only a full day/week so I just don't show up that day. Other times I just sit out and watch. Though that only happens when I don't want to, I've sparred many times.