I’m sure it’s fine.
The “fresh” salsa sold in the refrigerated section of your local supermarket would have gone noticeably bad long ago. Commercially sold salsa in glass jars generally has some preservative in it so that it will preserve its freshness in the fridge for a long time even after opening. (I’m sure that some will say that the preservatives themselves make it unsafe to eat, but I don’t hold with that crowd.)
I use two-month old salsa all the time with no ill effects. If it gets so old that it separates or congeals, then I’ll toss it, just as if it has mold on top. (Even then, I think it’s more of an “appearance” issue, but that’s an appearance I won’t tolerate.)