There is a VERY hard "I" that Lindsey Graham does. I think that's the specific version you're talking about, and that one is intentionally offputting. It's like "EYEEE RACK", but that does sound different from "AYERAK" or "EYEROQ".
The effete "ih-RAHN" is the NPR voice that you mentioned might get side-eyes. This is the closest to how Iranians that I know pronounce it, except that we don't have a phoneme quite like their R, which to my ears sounds like a D, L, and R all smashed together.
But these side-eyes are mostly fair, I think. It's like Americans prounouncing France as "Frawhce", or Paris as "Pahdee". Ostentatious and pretentious, for an English-speaker.
And Lindsey's provocative "EYE-ran" is very present in some locations, I think because GHWB and GWB's affected pronunciations were pounded into the American consciousness during Gulf Wars 1 and 2. Although Reagan did it too, IIRC, and I'm not sure about Clinton.