photographers used to use UV filters on their lenses to help protect them against knocks without any issues with colour.
Not sure why AABM has used past tense here. Most pros still use UV filters to protect their lenses. In the visual light range, good UV filters behave like clear pieces of glass. They don't impart color casts and don't make footage look washed out. I'm a long time commercial photographer with thousands of dollars worth of pro lenses for my ground based cameras. Many of those lenses are at least 5 years old, and some are over 10. I never use them without filters (except for my Nikon 14-24 f/2.8 which, alas, does not accept a filter). Scratches happen. Scratch your filter...no big deal. Scratch the front element of your lens, you are in for a costly repair. This is even more of a concern for X5S lenses, due to the debris that sometimes flies around during take off and landing. I've had to replace the filters on my Olympus glass for my X5S from time to time due to scratches, and this is much cheaper than getting a new lens. I've been using B+W filters for years, and they are great, but a bit pricey. I have recently started using filters from Breakthrough Photography, and recommend them too.
Returning to the original question, the only way that your UV filter would cause you to be getting washed yellowish footage is if something is wrong with it. Take it off and look through it. It should look like a totally clear piece of glass. Look at the shadow it casts on a white piece of paper. The glass should cast almost no shadow and add no color cast.. You can, of course, shoot some footage with and without the filter and compare that, as long as you keep your unprotected lens safe while doing so.
It is likely that the look of the footage you are getting is a result of the settings you are using. Perhaps you are shooting in D-Log? That looks quite washed out until you properly grade it. Check your video style setting, and of course your WB, which you should always set to a specific temperature or one of the presets like Sunny. There are lots of youtube videos out there with tutorials about how to adjust video and WB settings.
BTW, there are times when you should use an ND filter instead of a UV one. But there are definitely times when you should NOT use an ND filter. Basically, ND filters let you shoot at slower shutter speeds than you could without them, without getting over exposed footage. This is appropriate for standard cinematic video shooting, where you should use a shutter speed that's one over twice your frame rate; so when shooting at 30fps you would use a shutter speed of 1/60. In bright sunlight that's often too slow a shutter speed to get a proper exposure, so you put on an ND filter, which cuts down on the light intensity, without impacting the light in any other way. But you don't need to use that slow a shutter speed when shooting stills, and doing so increases the risk of motion blur, so it's actually not best practice for stills. And if you want to pull sharp stills from your 4k videos then you might prefer to shoot your video at a faster shutter speed too. Many people don't even notice when video is shot that way.
Hope that helps, and good luck!