It depends
Catholic doctrine holds that a completely gluten-free host is invalid matter, so low-gluten hosts are used instead. These test at roughly 56 ppm, which is above the 20 ppm gluten-free threshold — but that works out to about 0.002 mg of gluten per wafer, an amount the North American Society for the Study of Celiac Disease considers safe. The number looks alarming and the dose is not.
Unleavened bread, and in the Catholic Church it is required to be wheat. The 2003 directive on the matter states that a valid host must contain "a sufficient amount of gluten to obtain the confection of bread without the addition of foreign materials" — which means a wholly gluten-free host is not valid matter, and no amount of good will at parish level changes that.
Because it is one of the few places where the honest answer is not simply "find a substitute". For somebody who receives Communion, this is not an ingredient question with a shopping solution attached, and treating it as one is the thing most gluten-free guides get wrong about it.
That 56.5 ppm figure is the clearest illustration in this whole lexicon of why parts per million is not the same as dose. A concentration above the gluten-free threshold, in an object that weighs almost nothing, delivers an amount far below anything shown to cause harm. It is the same arithmetic that makes a trace in a large portion worse than a higher concentration in a tiny one.
CiCi reads an ordinary communion wafer as wheat, because it is. The low-gluten host is a different product and the distinction matters — the point of this entry is not to warn somebody off Communion but to make sure the thing they ask their parish for is the one that has actually been tested.
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.