We've received a few inquiries over the years about the availability of cotton tallits. Some people need to avoid wool because of a skin allergy, and a few are hardcore vegans who don't want to use animal products at all.
Very recently, a high quality cotton tallit, similar to traditional wool tallits, became available. I was quite impressed by the design and the weave. It's made by a long-established, highly reputable tallit and tzitzit maker in Jerusalem. Until now, the only cotton tallit option I know of is a hand-woven cotton tallit made by Gabrieli or another hand-weaver. But hand-woven is not really an option for those who want a very traditional design or an affordable commercial tallit.
The introduction of the cotton tallit is a big boon. For decades, acrylic has been offered as a low-priced alternative to wool. But it's quite problematic from a halachic standpoint, to the extent that a few years ago Mishkan Hatchelet, one of the world's leading tallit makers, abandoned their line of acrylic tallits, although they were hot selling items within certain market niches.
The new cotton tallit offers quite a good solution for those who want to avoid wool for whatever reason, or want a very affordable option that is not a big compromise from the standpoint of halacha and quality. In fact, we've even seen some interest among kollel men.
The manufacturer, KeNesher Tallitot, which is based in Jerusalem, is a reputable, longstanding company. KeNesher (formerly Hershkovitz) points out that their cotton tallit does not require dry cleaning, and can tolerate ironing.