Did exercising cause a stitch to spit? And when can I safely resume crossfit/weight lifting exercises?

Spitting sutures can happen as the deeper stitches migrate more superficially and do not dissolve. It likely has nothing to do with the exercise.

The strenuous exercise would have been a big factor with the spitting. Usually, patients are advised to wait until the incision has fully healed before returning to exercise. However, be sure to start with low-intensity workouts then gradually increase your intensity so as not to stress your incisions again. Your surgeon would be your best resource for information regarding these matters.

It is not unusual to have spitted stitches and it may be that a combination of this and excessive exercise led to the separation. Best to run your question past your PS but once healed you should be able to restart exercise - but take it easy initially and build up gradually.