Modern automotive body panels are 22 gauge (0.8 mm) mild steel. Double butted steel tubsets are usually between 0.6 and 0.4 in the thin areas, but use a much higher grade (stronger) steel. A little caution is advised, but it's not like the walls will collapse if you look at them funny. With less abrasive media and/or lower pressures, media blasting is a completely safe method of paint removal for steel bicycle frames - and probably much less risky than a grinder or coarse power sander. Powder coating almost always starts with media blasting the frame.

But my advice for people looking to re-paint a bike frame is always: "don't". It's a huge time sink and it's really hard to get a good looking result that lasts. The two most effective techniques are catalyzed urethane automotive paint (expensive, needs high end equipment, requires lots of prep) and alkyd enamel brush painting (inexpensive, minimal equipment, requires lots of time for prep and application). Both use standard automotive prep techniques (etching primer followed by repeated application of conventional primer followed by wetsanding), but the tight angles and small diameter tubes make good spray application a real challenge. It can be done, but you'll be amazed how much time it takes to do it right compared to a (relatively) flat automotive body panel.

The best solution is powdercoating. It costs about the same as a urethane paint job but needs virtually no prep work and is significantly more durable than most other finishes.