The most popular fabric choice for do-it-yourself pop filters is pantyhose or nylons. The material stretches easily over reasonable size frames, and instantly provides a double layer of material with air space between, and has very little effect on the range of frequencies transmitted. The layers of nylon block extremes of air movement, breaking up direct blasts and diffusing the energy. Though stretched, the material is not so tight that it resonates at an audible frequency, nor so loose that it flutters.
Not technically a fabric, foam of various thicknesses can be employed as a pop filter. Many microphones are sold with foam socks which fit snugly over the microphone, useful as dust covers for the mics as well. Foam performs the same job as nylon though not as effectively, and it is not acoustically transparent. Some high frequencies are blocked, but this can be useful if you are working with a singer with a lot of sibilance to her voice. Harsh "S" sounds can be reduced, as well as popping from hard consonants.
Any fabric with an open weave should have little effect on the frequency of transmitted sound. However, the weave may not reduce air passage enough to prevent pops. You can test a fabric for effectiveness by blowing through it. Most, but not all, of your breath should be blocked. If it is completely blocked, there may be some acoustic effect as well. As will foam, this may have some positive effect on certain vocals.
When working outdoors, wind blowing over a microphone is an issue, as the wind itself will create low frequency transients. News teams often use directional mics covered in fur socks. The length of the fake fur more aggressively dissipates the movement of air hitting the microphone. For a do-it-yourself project, the base of the fake fur material is important in its ability to transmit sound. Unless you frequently record outdoors, do-it-yourself fake fur pop filters are overkill.