If there were a person, let's call them X, who directly is conscious of other people's minds, then X has a default refutation of solipsism available. Let us suppose that not everyone is like X. However, let us also suppose that X and some of these others get into an argument: X says, "I directly am conscious of your consciousness." What can the skeptics say against X, though? X can no more be wrong about the existence of the skeptics' consciousness than they can be wrong about being conscious of various color patches, etc. (C.f. the private language argument.)
Now suppose that the issue was honesty, as in someone claiming to be like X: are they lying? But to attribute dishonesty to them will mean attributing a mind to them. We can't respond to an X-claimant without representing them as able to respond to our responses, can we? If attribution of a mind to an X-claimant is unavoidable even when the X-claimant is lying, it almost seems as if the X-claimant is vindicated in another way regardless.
So imagine that we have a Moorean or Rossian faculty of moral intuition, which delivers results pertaining to obligations we have to other people. Then we are not so far from being like X, it turns out. This might be a strike against the theory of a moral-intuition faculty, or it might be a strike against solipsism-via-skepticism. But if we have a priori reason to believe in obligations to others, without first representing those others as real other-minded people, perhaps there is some noncircular, rationalistic way to get at the existence of other minds even so.
Regarding that radical solipsism according to which the whole of reality is projected from just our lone mind: however, we are conscious of our minds as divisible into some sorts of "parts." It is less correct to speak of just "the mind" just like that, and more correct to speak of various faculties, drives, forms, levels, etc. Then we are conscious of our will as something other than our perceptions, for example. Now which compartment will we privilege as the projector, here? If we prioritize the representation of our will, yet then when we experience, in our perceptions, things that go against our will, we will be representing our perceptions as if they are another mind altogether, or house such a thing. Even if radical solipsism were (possibly) true on one level, on another it would then seem to be false (any one mind can be interpreted as a multitude of minds itself).