If someone is careful about only eating dairy which is Cholov Israel, is it OK to use a microwave which has been used for Cholov stam, without doing anything to kasher the microwave or wrapping the food?
The details of this kind of question are discussed in the Shach Y.D. 119 s.q. 20. The upshot is that no, it is not OK. Only if someone were microwaving food for a group and a person happens to partake, would there be a reason to be lenient (there are still other factors involved, but that is where the heter starts - you can't just use it yourself because others have a more lenient opinion).
The Shach is rather involved, but this is how Rabbi Yossef Slotnik explains it.
(NOTE: This presumes that a microwave requires Kashering at all - that is not universally agreed upon, and it presumes that the keeping of Cholov Yisroel isn't just as an extra Chumra. If the latter were the case, there may be further reasons to be lenient in extenuating circumstances).
If it is because of keeping it as a chumra (as do many in the United States) then one can even use the milchik utensils and pots used for Chalav Stam as long as they are clean. This is from the psak of a rav with Yoreh Yoreh semicha who keeps Chalav Yisroel and Bais Yosef shechitah as a chumra but eats in my house with no problem (I do not keep either).
According to the OU's website, if you double wrap food for use in a microwave, it can even be cooked in a microwave oven which has cooked non-kosher food.