do these really take off all the strain from the shoulders?
No. No shoulder exercise does that, because the entire point of a shoulder exercise is to apply stress to the shoulders. That's what exercise is, the deliberate application of stress to the body performed with the intention of driving the body to adapt and become more resilient to such stress.
However, the shoulder is also an enormously complex joint, with a dozen or more muscles crossing it. If only one of these muscles (or their tendons) is the problem for you, then it may be possible for you to perform exercises that do not stress that particular muscle. This will be enormously individual, and you would need to be experiment conservatively with different exercises and see which ones do and don't aggravate your injury. But there's no exercise that is "safe" for all types of shoulder injury, it would depend entirely on what you as an individual can tolerate, and something that was fine or even beneficial for someone else's shoulder injury could worsen yours.
I think I’ve messed up my shoulders a bit from muscle ups and (mainly) jiu jitsu… doctor says rest them for a couple of weeks.
Have you considered following the doctor's advice and just not doing any shoulder exercises for a couple of weeks?
Deadlifts seem like they’re also out cause you’re pulling on them.
You're not actually using the muscles of the shoulder in a deadlift, except for a bit of contribution from the lats pulling the bar in close to the body. The weight is supported by the ligaments of your shoulders rather than the muscles and tendons, and unless you're recovering from a surgery or dislocation, it's unlikely that your ligaments are what's in need of rest.