As stated already, there is a degridation, but with a good filter it is minimal and not worth losing any sleep over. Were it gets progressively worse is if you start stacking filters. If you stack a CPL on your UV filter, the IQ hit gets worse and it may start to be noticable. If you add a third filter (e.g., ND or GND), then you are getting into noticable degradation of the IQ.

Protection from dust, salt spray (sea side shots), scratches from cleaning, damage from dopping, etc., can be costly without the filter.

I would suggest leaving a good UV filter on uless you are going to use another filter. If you use another filter, it should be on a bare lens. If flare is an issues, then you may want to try the shot w/o the UV filter to see if it helps (becasue cls is correct, flare can be worse with the filter).