As far as we know, it appears that the New Republic, and by extension the Resistance, did not have medical stations like the GAR did, but they certainly did have dedicated medical facilities. A military force can’t function without them. Since the Resistance works out of ships and small planetary bases, that is where their facilities are located. They owned at least one modified Nebulon-C escort frigate, which they used as a medical frigate. The NR had more options, as a legitimate government, and though we don’t know of any it is possible that they could have had medical stations at their disposal. If they abandoned the idea, it would probably not be because of any risk associated with it (since any medical facility or vessel is going to be vulnerable to attack), but perhaps because they no longer needed them after the demilitarization and such a long stretch of peacetime.
Hope that helps!
~ Jacen