Lens rentals tested a lot of filters to answer your question. Basic conclusions below. From their testing...yes it impacts IQ to varying degrees and brand/cost isn't a big factor in whether a filter impacts IQ and to what degree.
This is subjective data, of course, and I gave you full-size images so you can make your personal opinion. But Aaron and I spend all day adjusting lenses by evaluating changes in these kinds of dots. We looked at them separately, and both had exactly the same subjective conclusions:
Filters that had no significant effect: All B&W, Canon Protect, Chiaro 98 UVAT, Heliopan Protection, Heliopan UV SH-PMC, Hoya HD Protector, Hoya HMC UV, MeFoto Lens Karma, Nikon Neutral, Tiffen Ultra Clear, Tiffen HC, Zeiss T* UV
Filter may have had an adverse effect: Hoya NXT HMC UV, Tiffen Clear;
Filter had a significant adverse effect: Chiaro 90 UVAT, Chiaro 99 UVBTS
Google lensrentals.com and filters and there are several articles.