I believe that Trump isn't bothered by Ilhan per se. What ticks him off is the hijab. Or more accurately, what the hijab represents. It stands for moral integrity, modesty, and bravery. A person who wears the hijab is openly declaring what they believe in and shows that they aren’t afraid or intimidated by peers or society at large. These are qualities Trump should have, but doesn't.
Keep in mind that Trump, like many Westerners of his generation and social class, likely had a Christian upbringing or devout Christian parents and grew up reading authors like Tolkien, C.S. Lewis, and Ursula K. Le Guin. Authors that often explored themes like humility, leadership, the dangers of power, and the battle between good and evil.
What really bothers Trump, I think, is that there's someone in the room who is better than him, someone who has stayed true to the values that separate real winners from losers. And we know how his whole personality revolves around being a winner.
My suugo psychological analysis of Trump.