If the SI joint is a weight bearing joint, I would say getting it used to bearing weight would be pretty important for recovery. Ligaments adapt to loading, and squats/deadlifts, presses would be the best thing to force this, in my opinion.
The SI joint is not a mobile joint (unless there is a ligament rupture) and sacrum movement is so minuscule that there’s no realistic way for someone to feel it upon palpation. If you don't have a rupture than there's no reason to do nothing. I find that squatting tends to quiet it down and "put things back into place" to use a colloquial term.
Again, not knowing you or your condition, I would start with very low weight and high rep ranges, trying to limit stress on the joint while allowing the joint to work through full range of motion. A good coach would help here because form is important when recovering from injury.
It takes awhile to get comfortable with the idea that you could experience repeated flare ups and still be making progress. We can spent too long pining for the day that we will be “cured” and never experience low back pain again. And each time we tweak our backs, we feel disappointed, like we're jolted back to square one. Keep it simple and play the long game.