Because they were, at the time, the most predominate minority race by a wide margin, most of the histories on American racism focus on the plight of the black community. How were Americans from the middle east seen in the early 20th century (and 19th century while we're at it)?
That is perhaps a broader question than you realize. The middle east region (defined loosely in the historiography as North Africa, eastern Mediterranean, Caspian, Persian Gulf, Arab Pen., into Pakistan perhaps) is a very large and diverse area. Even within one country, say Iran, there are several ethnic groups, major languages, skin tones, religions, etc.
So, to get to your question, it's complicated and there is not one answer. There was, of course a lot of orientalism going on with white Americans appropriating or romanticizing different cultures from the MENA region. But you did have a population of ME'ers, especially Syrians and Lebanese, in America. Pre-immigration quotas of the post-WWI era these populations grew, brought families over, and came to work in the ballooning Fordian industries. Pretty soon the US cut off immigration from the area, creating a community that was once cut from its home but also in many ways became more Americanized. You saw Syrian Muslims in Detroit, for example, painting their mosques and cultural centers as churches for the benefit of their white neighbors. In that region with the automobile industry, ME'ers often lived in white areas as opposed to black areas. Later, there were more (esp Arab) waves of immigration from the ME and a post WWII McCarthy era made Americans more suspicious of ME'ers, especially because many identified or sympathized with Israel as opposed to Palestine.
For some great background reading, try Sally Howell's Old Islam in Detroit.