If it hurts, don't do it.

There are PLENTY of other things you can do that won’t cause pain. If you have a bad shoulder, go get it looked at by a professional. You have another arm, two legs, a core, and a cardiovascular system to train while you let the injury rest and rehab.
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As an example, let’s say you slammed your hand in a car door - ouch! After waiting for it to heal, do you go do it again? NO! Hopefully you’ve learned from the last time, but many of us do this with injuries. We get hurt deadlifting, we rest, we rehab, then we go right back to deadlifting the moment we’re pain free. The “no pain, no gain” mindset is an outdated manifesto.
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Pain is the brain’s way of telling you to stop and evaluate - kind of like the check engine light in your car. “No pain, LOTS to gain” is our manifesto. Let’s treat the pain and use that time to train non-painful muscles and other systems while creating mental fortitude by focusing on what we can do, and not on what we can’t do.