A lot has been said to demonstrate the reasonableness of belief in the non-physical. But, if we know of things (such as the mind) which are not physical, we have very good reason to think that the physical senses don’t exhaust all ways of knowing.
In fact, real-world personal experience is our most fundamental way of knowing about reality. It isn’t perfect, of course, but gives us a basic sense of what exists.
That being the case, there is no good reason to throw out the idea of moral truth.
For every argument that there is no such thing as objective moral truth, a parallel argument could be made that there is no such thing as physical reality. It really makes no sense, then, to insist that we trust our physical senses, but not our moral sense.
One might say, for instance, that not everyone has the same moral senses–or that different cultures have different values. But this strikes me as no different than saying that green is a shade of blue in Japan, or that the sky is bronze according to the ancient Greeks. If this is not a reason to think that our sight is completely untrustworthy as a sense, it should not be a reason to reject the moral sense.
Or, one might say that there is no reason to believe in moral truth other than our moral sense. And this is no different from saying that there is no reason to believe in the physical world other than our physical senses. People have always trusted our basic sense of reality until we have a good reason not to.
There are a number of these arguments, but none of them establishes that moral truth is any more questionable than physical reality.
That being the case, the modern tendency to embrace moral relativism, while scoffing at solipsism, seems more a cultural assumption than anything which has been defended on logical grounds. Really, I doubt it would be accepted at all if not for the stereotype that relativism is the position of educated people.
And it is more a stereotype than reality. College professors are consistently less relativistic than their students. And the philosophy department (where specialists in ethics reside) are the least relativistic of professors. That being the case, the rhetorical force that relativism is somehow the sophisticated view loses its force.
So, to move on from stereotypes and rhetoric, philosophies should explain our experience of life, not call it illusory. I think we have a basic sense that causing pain, or refusing to help those in need is wrong–and that loving others and seeing to their needs is good. Dismissing these rather obvious truths as illusory would be trying to fit the facts to our theory, rather than the other way around.
But, if one sees the reality of moral truth, one is left trying to explain why it should exist. And that, I would argue, will lead one toward theism.