Prolonged and direct exposure to UV light can be harmful to the eyes. This is generally a concern only for cleaning staff who use the very bright Professional Urine Finder on a regular basis. With the consumer model (or Mini-LED Urine Finder), the output is not so bright as to cause a problem in ordinary use, though caution should be exercised in never looking directly into the light.
As far as protective eyewear goes, most modern prescription glasses include a UV coating. Inexpensive safety glasses from the hardware or home-improvement store also generally include a UV coating –check the product labeling to be sure.