Right, DOT 5 won't mix. However, it is compatible, the two can co-exist peacefully. In my experience, it seems that the non-DOT 5 absorbs not only the purple dye, but also any moisture and wear particles, etc. such that it eventually turns into a black goo. Unsightly, but doesn't seem to present any problem except perhaps (if it settles inside a caliper) boiling easier than DOT 5.
DOT 5.1 is not silicone, and will still eat paint, absorb moisture, degrade over time and so on. Better than DOT 4 (higher BP and all), but not as good as DOT 5 (for our old cars, IMO).
I agree that "best practice" is to replace all the seals, soft lines and so on. Preferably using the SS/teflon soft lines instead of rubber. (Good time to think about replacing those antique hard lines too.)
However, I'm not convinced that it is always essential to do so. For example, I converted a 1980 Chevy to DOT 5 in 1988 by just bleeding through at all 4 corners until clear purple fluid came out. One caliper was replaced (it was leaking before), everything else remained original. I never touched the brake hydraulics again, they were still working perfectly when the car was junked in 2005 (with roughly 250,000 miles on it).
If you do want to flush the lines, you might consider using brake cleaner rather than rubbing alcohol. It's a much better solvent, and unlike rubbing alcohol, doesn't contain water. Personally, I wouldn't use shop air either, as it is often contaminated with water and/or oil. Or at least use a filter on it.