You might say that Donald Trump is a bit Islamophobic. But, rightly so. He has a nation to protect. If he didn't, he'd probably be Islamophobic all the same though. The very threat of a certain nationality and religious group who is known for killing millions, including Americans makes it difficult for a president not to be overly cautious of them.
If Islams were not a violent type group, some of them at least, there would be no worry from Trump or others about them. The fact that 9-11 occured is proof that the fear is realistic and any president should be concerned about the well-being of their people.
Obama was not. In fact, it was speculated that he had close ties with them and some proof exists that he did, infact. That is even more reason for Trump to be overly cautious in the area of Islamic people which is really what Islamophobia boils down to.