If it's chronic back pain, and my back is not in a spasm, then yes, I workout around the pain. If I stopped working out every time my low back nagged me, I'd never work out.
I recommend you do these every single morning after you get up from bed...well, after you pee. It only takes a couple of minutes, but it works wonders for chronic low back pain.
I do the bottom stretch between sets. I also do this thing that looks like a cat hunched back multiple times also between sets. I seen it used in yoga. It relieves the compression feeling in my back. I do it sitting down on the safety bar of the the rack while leaning over to not look like a weirdo.
ialso stretch my hip flexors and hammies real good before squatting.
My back is fucked...cant deadlift or back squat. But I can do front squats, light dumbell Romanians and walking lunges.
So yes, I work around injuries. I simply have to if I want to work out.