I don't have a "red dot" on a CZ 75 Compact model but I do have one on my P07, which is considered to be a compact?? At least it's not a full sized gun, like the P09.
I carry that thing just about everywhere (meaning I don't carry it into the county courthouse or any government building (they are comfortable taking my tax dollars but not with me being able to defend myself, go figure).
Day in, day out. Shopping, driving the car/truck, mowing the grass, walking the dogs, fishing, etc. I carry it mostly in a concealment holster rig called an Air Marshall 3. I sometimes carry it in an inside the waistband holster on my right side. Depends on where I'm going, what I'm doing.
No issues. Meaning the gun itself (the butt) is more likely to show the gun is there than the RMR mounted to the slide.