A filter will degrade quality...
Yes, a protective filter will degrade the image quality of a lens but, the question is, "Is the amount of protection offered by a filter worth the amount of quality lost?"
The answer is a definite MAYBE!
It would depend greatly on the venue and lighting in which you are shooting; the quality of filter used and the image quality which you will accept and whether you are using a correct lens hood.
I tend to take a mid-way stance and use a protective filter whenever I am in a venue that would be possibly harmful to my lens such as blowing dust and sand, precipitation or any other dangerous element. I always use a lens hood and when I do use a filter, it is always a top-line model such as B&W or the Hoya Multi-coated models.
BTW: I have never seen an objective measurement such as an MTF chart regarding the loss of image quality when using a protective filter. I would love to see some objective testing.