I have had this happen to me. I bought these: head bands. I don't have a problem with breaking out.
I use my Q2 for workouts all the time. Supernatural, mostly but I work up a sweat doing Beat Saber and even Superhot. I don't think there's a danger of damaging the unit from sweat, but it is gross. I would recommend 1) "fitness" facial interface from VR Cover or Kiwi (I've used both and they're pretty much the same) and 2) thin headbands like these. Also if you have a floor fan, that helps too.
I have not used a treadmill but I think it might be okay as long as you have good balance and spatial awareness. I would walk, I'm not sure I would run though. I have used an exercise bike and thought that was pretty good, though sometimes sideways motion would cause me to lose balance - not a big deal on a stationary bike, but not a great feeling.
You do not need to buy all these expensive brands to get a great fit. I got these on Amazon and they’re great! Hold A LOT of sweat. I’m a woman and the mens still work fine.
Vinsguir Mens Headband (4 Pack), Sports Headbands for Men, Workout Accessories, Sweat Band, Sweat Wicking Head Band Sweatbands for Running Gym Training Tennis Basketball Football, Unisex Hairband https://www.amazon.com/dp/B07XXZ5ZGK/ref=cm_sw_r_cp_api_glt_fabc_9HCHDNFHZQ41S9MNTVTC?_encoding=UTF8&psc=1
I've worn these from Amazon underneath my helmet while mountain biking and they work great. Hold a ton of sweat and affordable.