More from the philosophy class. As I reread this just now I didn’t really answer the whole question. Although, I amended it since in the class forum.

What does it mean to say that the concept of God is simple? Can this claim be held together with the claim that God has attributes? If so, how? If not, is this a problem for theism?
The concept of God as simple simply entails that the God conceived of by folks like Aristotle, and Thomas Aquinas, Maimonides et al. is a Monad. I.e., a non-composite being who is not made up by its parts or properties in addition, but a singular substance who is also identified, within this complex as an actus purus (āpure actā), pure being, unmoved mover so on and so forth. It is this construct, as in this case, exemplified and articulated in the tongue of Maimonides, that all of the so-called Abrahamic religions (Judaism, Islam, Christianity) can have a shared starting point in their respective God-talk.
As noted by Maimonides, his knowledge of God, after Aristotle and the philosophers, is arrived at by a process known as the via negativa (negative way). This speculative process is undertaken, as Maimonides develops, within an apophatic frame for thinking the ineffable God. That is to say, that God is so necessarily hidden in this frame, that all the would-be knower of God is left with, at a basic or primordial level, is to engage in a process of negating the seen, the āknown,ā like the negation of nature in general, or even human being in particular, and to think Godās perfections or attributes, from these speculative means; as the philosopher works their āway upā the supposed chain of being; whose first cause, is indeed the unmoved mover, the monad known as God.
Christian theism alternativelyāand I use that language in a particular way, noting a trinitarian way for thinking GodāI would argue is necessarily a kataphatic (versus apophatic, in a sense) religion. That is to say, Christian theism thinks God first, not from a negation of human being, or nature in general, but from Godās Self-revelation in Jesus Christ. John 1:18 says: āNo one has seen God at any time;Ā the only begotten God who isĀ in the bosom of the Father,Ā He has explainedĀ Him.ā The word translated as āexplain,ā in the koine Greek is exegesato, to exegete, to āread-out.ā Indeed, even in this passage there is a sense of apophaticism in God, that is to say that He indeed is a hidden God. But to the point, on the Christian account, God freely chose to Self-reveal and explain Himself in the face of His Son, Jesus Christ. This is why Christians first think God not as a faraway pure monadic being, but as our Father (as Athanasius emphasizes: āFather of the Son, Son of the Fatherā). A genuine Christian theology works from a via positiva (āpositive wayā) towards thinking God. That is, from revelation rather than speculation.
In the end, classical theism, and as that has been appropriated by certain traditions within Christianity, does take on the type of thinking that Maimonides articulates in regard to divine simplicity; and āitsā methodology. And yet there are other traditions, like the one I affirm, within Christianity, who think God from within only positive, Self-revealed terms; indeed, as the base of a theological methodology itself. And yet all orthodox Christians, at some level, will affirm that God is simple (non-composite). Even so, there are other more relational ways to engage with that notion. My teacher, Karl Barth, evangelizes the concept and re-terms it as āDivine Constancy.ā But that requires further development, and more space than available at the moment.