My answer is that in the US, the "crepe" in crepe fabric, crepe paper and crepe rubber is always pronounced /kreɪp/, but that the name of the thin pancake is is pronounced both /kreɪp/ and /krep/, and both pronunciations are common.
In the case of English words borrowed from French, in the United States it is very common to hear two different pronunciations--one Anglicized, and one approximating the French pronunciation. For example, the "en" in words like "envelope" and "envoy" may be pronounced to rhyme with "hen" (Anglicized), or like the word "on" (approximating French).
People who have studied culinary arts, people who have studied French, or people who write it with the diacritical mark as crêpe would likely approximate the French pronunciation and say "/krep/." But many pronounce it the same way as in crepe fabric, crepe paper, and crepe rubber, and pronounce it "/kreɪp/."
The American Heritage dictionary gives the pronunciation as /kreɪp/ for crepe fabric, crepe rubber, crepe paper, and but adds the note "also /krep/" for the pancake.
My wife and I are both native US speakers. I would say /krep/ for the pancake, but I just asked my wife what she says, and she says /kreɪp/.
I think the Anglicized pronunciations are becoming more and more common.