It depends
Most modern blue cheese is cultured on a gluten-free medium and tests clean. The residual concern is producers still using a wheat or rye bread substrate. Testing published in 2018 found the risk is real but uncommon.
Cheese ripened with a Penicillium mould — roqueforti for Roquefort, Stilton and Gorgonzola, glaucum for some others. The blue is the mould growing along channels pierced into the curd. The cheese itself is milk, salt and culture, none of which has ever contained gluten.
Because of how the mould used to be propagated. Traditionally the starter was grown on rye or wheat bread, left to go mouldy in a cave, dried and ground — which is a real historical practice and the origin of a caution that is still widely repeated. Modern commercial Penicillium cultures are grown on defined laboratory media rather than bread, and most are nowhere near a loaf.
Testing has consistently found blue cheese at well under 20 ppm, including cheeses whose cultures were bread-grown, because the mould is a tiny fraction of the finished cheese and the protein does not survive the journey in any meaningful quantity. The practical answer is that plain blue cheese is fine. What is worth checking is the things made from it — a dressing, a dip, a sauce — where the risk is the thickener rather than the cheese.
CiCi treats blue cheese as conditional rather than safe, which is deliberately more cautious than the evidence strictly requires. It is a small category, the historical practice was real, and an explanation of why the caution exists is more useful than a bare yes that leaves somebody wondering whether the thing they half-remember was true. It was true. It mostly is not any more.
Every one of these is the same ingredient. The number of names is a large part of why gluten slips past people who read every label.
Point CiCi at the barcode on the product you're holding and get this same reasoning in about two seconds, plus the carbs and the full nutrition panel. 360,000+ packaged foods are already read and waiting.
This answer comes from CiCi's ingredient lexicon — the same rules the scanner uses, not a separate article. Where reputable sources disagree, CiCi takes the conservative position and says so.