Did they face racism? Yes, Hispanics (and I'm mostly referring to Puerto Ricans here) reported facing similar prejudices as African Americans. Those reporting to duty on the mainland faced segregation among themselves into either white or black troops, they weren’t segregated by themselves the way African Americans were. The 65th Infantry Regiment, nicknamed the Borinqueneers was made up entirely of Puerto Ricans, their nickname coming from the original native name of the island. There was a recent documentary about them that you might want to check out.
For a more general picture specific to Hispanics and WW2, l recommend the following: