I’m brand new to this page so bare with me. I bought a new fridge over the summer in my home,and it didn’t have an ice-maker in it, so I didn’t run any water line from the valve to the fridge since it wouldn’t serve any purpose. The old supply valve leaked so I put a new one on,no leaks on the new one,and I also put a cap on it just for safe measure even though I have it shut off. That is my question though for this,is if it’s okay that the fridge valve stay closed like this? There is no ice-maker nor any water dispenser on this fridge,so the valve is just there staying shut off until I may add an icemaker to it in the future. I just want to make sure I’m not hurting my plumbing by keeping that valve off? I’m sorry if the question is dumb,I’m a new homeowner.
Saddle valves (the self-puncturing valves often used to feed water to icemakers, mostly because they're easy and quick to install) do have a bad habit of coming loose over time and leaking. Your new one, if it's that type, may eventually do the same thing. You could replace it with a more serious valve next time a leak develops.
... but for now, you've got a perfectly reasonable fix in place. No, it isn't doing any harm.
Enjoy the new house (and the new hobbies you're going to acquire while taking care of it)!