I didn't vote since I can't answer one way or the other definitively.
For me, it would really depend on the reason. Let's say I had to start taking Warfarin (blood thinner) due to a DVT episode from all my flying. Then I would wear a pair of minimalist shoes to protect myself from getting cut and bleeding to death on a run. If it was more due to structural (bone, muscle, tendon, etc), then I would probably give up running and switch to biking.