For DV applicants, yes. They are subject the same requirements of not being a public charge as any other permanent resident. For refugees, they get a year to support themselves before they file the I-485. And illegals - surely you are joking?
I am sorry I do not know the laws about specific category of visas and when they are allowed to be public charge and when not.
But the point is ... once a person has satisfied the requirements, they should be allowed to get the benefit given to all people in that same category.
What you need to look at is the laws and their implementation, not an individual trying to get the best benefits as allowed under the law.
So if 60% of the benefits are in one category, then figure out how you are going to fix it. But do not say that this one person is going to make that number 60.001% and hence that is bad. The 60% is the problem, not the 0.001%. Yes, each 0.001% adds up to 60, but the idea is to make macro changes ...
So if a state program offers medicaid for GC holders ... why would we rabble rouse against an individual, you should be telling the state to stop it, but telling the individual on which forms to fill up to get the aid, and also provide a list of most preferred states to get such an aid.
To give an example on similar lines ... I so much like the Arizona (and now Georgia I believe) program to fix the illegal problem as best as they can. However, as hypothetical, if Maine gives a drivers license to anyone without any proof, while I not like the person who was trying to abuse it to get a DL, the fact remains that the bigger problem is the state.
To give another example ... what is wrong in publishing a list of states where radar detectors are allowed. We all know what they are used for, at least in 99.99% of the cases. The problem again is only partly with an individual using it, but the bigger problem is with the state.