I work for public institutions, and I've had a couple of these with UC/IBD and mildly elevated blood pressure. They've been of no consequence. In fact, the last one many years ago seemed just to confirm that I am actually a living, breathing human being and not a trained chimpanzee.
I've since become involved in several candidate searches, and I've learned that HR/ legal's primary motivation is the TB test. Any pre-existing conditions cannot be factored into any hiring decision, but the physical is used to assess our group rates. Medical records are also to be kept partitioned from HR files (by law, if I'm not mistaken).