This Washington Post article attempts to clarify the theological issues surrounding Wheaton College's decision to fire Larycia Hawkins, but I remain confused after reading it.
According to the article, Wheaton College decided to fire Professor Hawkins on account of her statement that Muslims and Christians worship the same God, and on account of the fact that Muslims and Christians have different views of the nature of God. Specifically, Christians believe in the doctrine of the trinity, while Muslims do not.
The problems with this explanation are twofold. The first is that not all Christians are Trinitarians, but non-Trinitarian Christians (such as Unitarians and Jehovah's Witnesses) are usually regarded as worshiping the same God as Trinitarian Christians. The second is that, more generally, it seems that Muslims and Christians (or members of any religion) could worship the same God (i.e., the same divine being) even if they have different theories about his nature (i.e., different accounts of the essence of that being). It is logically possible for different people to have an attitude towards or relationship with the numerically same being even if they have different beliefs about the being's ultimate nature. By analogy, a brother and a sister could both love their father if they had different beliefs about their father's character, or even about his underlying nature as a substance.
In fact, Muslims claim to worship the same God as Jews and Christians (the God of Abraham), they accept all of the same patriarchs and prophets as Jews and Christians (excepting only Muhammad), and they even accept that Jesus is the Messiah--so it is difficult to make sense of the claim that Muslims do not worship the same God as Christians. There are many disagreements between Muslims and Christians, but they do not appear to be in disagreement about which God they worship. (The matter is otherwise, for example, with Hindu monotheists, who do not universally identify the one God they worship with the God of the Hebrew Bible.)
Having said that, it is well within the rights of Wheaton College to fire a faculty member for not adhering to their theological requirements, but it seems they should do a better job articulating what those requirements are and how Professor Hawkins has violated them.
What is made clear by the Washington Post article is that there have been several previous incidents in which Hawkins has offended the scruples of Wheaton College administrators, but the previous issues have more to do with politics and morals than with theology per se. Wheaton College should have the legal right to fire faculty who do not maintain their preferred political or moral beliefs, but it seems disingenuous to fire someone over an alleged theological dispute if the real problem lies elsewhere.
Update: Edward Feser already tackled this issue in much greater depth at his blog, and again in a recent post.