Is "close proximity" a tautology?

"In close proximity" is redundant in one direction, but not in the other. Semantically, "close" adds something to "proximity," but "proximity" adds nothing to "close," but it does provide a convenient noun form to tack onto "close" when one's mouth is in gear before getting the words straight. (It also adds a dash of formality and a few extra syllables for city councilors and police chiefs at press conferences.) The cognates of "proximity" carry a sense of figurative nearness, as in Aristotle's "proximate genus" and "approximate." These do not involve spatial nearness, and "proximate" is most frequently encountered in theoretical contexts. "Close" is more primarily a spatial concept. "Close" also describes a space that feels tight and cramped. "Proximity" signifies a vague kind of nearness: abstract, spatial, and not as tied to the scale of ordinary human sense-experience as "close." Even when restricted to its spatial sense, "proximity" suggests in a matter-of-fact way that the the distance involved is relatively small, while "close" suggests additionally a humanly-felt nearness. It's in the connotations that "close" adds a bit of emphasis to "proximity," though "in close proximity to" can be replaced by "close to" with no loss of meaning.

Given that a third of all NGram instances of proximity over the last century occur as close proximity, I think one can reasonably say it's a common idiom (at least, common relative to the word proximity itself). You can't just reject an idiom on the grounds of "illogical" tautology. When assessing this chart, bear in mind proximity instances include close proximity, so the relevant ratio is what's under the red line compared to what's over it.