It is a simple point of logic that if propositions p and q are both true, then they are logically consistent, though not conversely. So if God exists and Evil exists are both true, then they are logically consistent, whence it follows that it is possible that they be consistent. This is so whether or not anyone is in a position to explain how it is possible that they be consistent. If something is the case, then, by the time-honored principle ab esse ad posse valet illatio, it is possible that it be the case, and my inability, or anyone's inability, to explain how it is possible that such-and-such be the case cannot count as a good reason for thinking that it is not the case. So if it is the case that God exists and Evil exists are logically consistent, then this is possibly the case, and a theist's inability to explain how God and evil can coexist is not a good reason for him to abandon his theism — or his belief in the existence of objective evil.
The logical point I have just made is rock-solid. I now apply it to two disparate subject-matters. The one is the well-known problem of evil faced by theists. The other is the equally well-known 'problem of mind' that materialists face, namely, the problem of reconciling the existence of the phenomena of mind with the belief that nothing concrete is immaterial.
The theist is rationally entitled to stand pat in the face of the 'problem of evil' and point to his array of arguments for the existence of God whose cumulative force renders rational his belief that God exists. Of course, he should try to answer the atheist who urges the inconsistency of God exists and Evil exists; but his failure to provide a satisfactory answer is not a reason for him to abandon his theism. A defensible attitude would be: "This is something we theists need to work on."
Atheists and naturalists ought not object to this standing pat since they do the same. What materialist about the mind abandons his materialism in the face of the various arguments (from intentionality, from qualia, from the unity of consciousness, from the psychological relevance of logical laws, etc.) that we anti-materialists marshall? Does the materialist give in? Hell no, he stands pat, pointing to his array of arguments and considerations in favor of materialism, and when you try to budge him with the irreconcilability of intentionality and materialism, or qualia and materialism, or whatever, he replies, "This is something we materialists need to work on."