Can I reuse mounting holes into a stud for a shelf?
Assuming that the screws don't feel loose when you remove them due to inadequate length or pilot holes that are too large, you can reuse the holes. I've done just that a thousand times with everything from knickknack shelves to solid wood doors. The point of concern usually isn't the holes, but the screws. If they were barely adequate before, they'll be risky now.

Since you haven't told us anything about the shelf or the screws, I can't be more specific than that.