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UV protectors - actually, any filter in front of your lens - can result in flare when shooting towards bright light sources, and can impact image quality in other ways... color balance, loss of sharpness, strange effects on out-of-focus rendering, etc. Often-times, these won't be immediately apparent, but when they are, they can be difficult or impossible to remove in post-processing. As such, I'd recommend you only shoot with any filter when you need it, or the benefits outweigh the risks.
I fit UV or clear protectors to my lenses when I'm shooting in inclement weather, dusty and gritty conditions, or when the front of the lens may get splashed, as I like to be able to clean the optics in the field with whatever I have available (often a shirt tail !!).