On push days I always end wit some cable isolation excercises for triceps, chest, and shoulders.  When I do lateral shoulder raises there is tenderness in my right shoulder the first rep of every set but it's fine after.  It's not tender with any push excercises whether it is targeting shoulders (military press) or not.  I think maybe I have some arthritis in my right shoulder.

The tenderness isn't bad and doesn't hinder me. I guess I'm not sure if I should just deal with it/accept it or avoid that movement altogether?

As long as it's not hindering you (especially to the point of being painful or negatively affecting other lifts or your general mobility), just push on through.

Do lots of stretching. It's great for the shoulders.

If I stopped lifting every time I felt some tenderness or pain I'd never be lifting and always resting.  You have to work through minor injuries to continue to progress.  My left shoulder has been bothering me for the last few months.  It's finally getting better, but I never stopped benching heavy.  As I age I start out lighter and don't make as big of jumps in weight as I work up to my working set weights.  Basically warm up more thoroughly.

Work around it, and address it.

I hurt my shoulder at work and it took forever to heal.

I couldn't press flat for months, but overhead was fine, so I did that.

Get in there and poke around a bit, see if there's any muscle insertions that are inflamed or trigger points that are balled up.

You train to feel better, not to feel worse. If something hurts, don't do it until it doesn't hurt.

I think it really depends. Like others have said, there's always going to be something. I would try to figure out what the actual problem is and get it resolved if possible. How long has t this been happening?

I just started lifting last summer after 10+ years of sitting on my ass. Within a couple months, my shoulder was killing me on the bench press. Rotator cuff issues. I took a week off, found some shoulder stretches and exercises and started doing those a couple times a week while returning to the gym and moving my bench press over to the Smith machine for a while. After a month or so, it was all good. Back to the regular bench, no issues.

After that, I started getting some minor tennis elbow. I thought I could work around it, push through it, etc. It worked for maybe a month, then all of the sudden my bench got weaker, my pull-ups decreased by almost half, and I started to plateau with other exercises. And it hurt to even pick up a glass and take a drink. I've since figured out I had a muscular imbalance, started doing corrective exercises, and am finally recovering - but that shit started in November and hit me hard and I'm still dealing with it. I should have taken a step back and figured this shit out after the first few weeks. I'd be 100% by now.

If it really is just a little arthritis, it might be fine to just keep going. But pay attention and, if it gets worse, then it's time to investigate further. A little stretching (mobility work, really, not cold static stretching) probably wouldn't hurt if you aren't already doing some of that.

I'll push into discomfort regularly, but pain is the body's way of letting you know to stop doing something. Skim the surface of pain now and then, but don't dive into it.

Just updating to say my shoulder seems to be better now.

Awesome !!!

I have a left torn rotator cuff and a right torn shoulder labrum (neither from lifting). I bench 375 and train regularly.

Shit flares up and hurts, and I use rubber bands for rehab and different movement patterns to deal with it.