Having an illness like the ones you mentioned above will immediately disqualify you from a lot of trades. Depending on the severity and manageability of the illness, you MAY not be able to get in at all.
For example, if you‘re a severely insulin-dependant diabetic, NO WAY. The military isn‘t able to provide for those kind of medical or dietary requirements. However, if you‘re non-insulin-dependant, you may have a chance.