Couple of things:
1. Legally, time to go to drill is protected by law. That being said, you would be a fool to not play nice with your program. They can hurt you badly and you would never be able to prove anything. Beyond that, you're just hurting other people in the Guard if you come through being a pain in the ass.
2. The flip side is that you are legally obligated to be at drill unless excused by your commander. They have full power to send the police to find you and bring you to drill. They too can hurt you, though frankly even a dishonorable discharge (let alone a less than honorable discharge) is probably less damaging to your career than being kicked out of residency.
3. You absolutely are deployable. Never mind that the US government, if sufficiently inclined, can draft and deploy whoever they please. There is nothing in the law that protects you from deployment. You're still extremely unlikely to be deployed to the point where you're better off worrying about spending the millions you'll win in the lottery. You're protected by politics and your own uselessness. Medical student and interns are useless, WW3 probably wouldn't see you activated. A resident, as someone who in many states can be licensed to practice medicine, could potentially be activated if something like WW3 were to come along. Barring catastrophe, even the military is not going to risk the fall-out from pulling reserve members out of their civilian training programs.
So what do you do? You work with your unit and program while accepting some personal sacrifice to meet your military obligation with minimal impact on your residency program. Some residency programs will willingly schedule around your drill weekends. Some units will barely require you to actually show up. The more likely situation is somewhere in the middle. Between the two you can usually find a workable solution: going to one day of drill 2 months instead of a full weekend 1 month, getting drill credit for attending a conference or submitting CME, drilling at a full-time medical unit during a weekday you have off, etc.
Bottom line, it takes some communication but you can make it work especially in a specialty like Emergency Medicine. Don't forget the 2 weeks of Annual Training currently required every other year. Again there are solutions like elective and/or vacation time. You just have to understand that the drill time is coming out of your days off not in place of shifts in the ED...
Frankly, most of the people in my program forget I'm in the Guard. I take it as a good thing.
