Acoustically transparent fabric may be found at Guiliford of Maine (800-544-0200). They are located in Grand Rapids Michigan. They have a large variety of styles, patterns, etc. etc.
All fabric sold for acoustic purposes will have an ASTM test report (in Sabines) or with an NRC rating (NRC applies only to frequencies above 4kHz). The level of transparency you require will depend upon your purpose ... obviously, if you're making speaker grill material, your needs will be different than using the material as a wall covering over acoustic panels.
If you find something you really like and it's not sold for acoustic materials you can apply two, ad hoc tests: (1) can you hold it over your face, see light through it and breath; and, (2) take up smoking and see if smoke will drift up through the fabric. It'll work (but not for speaker grill cloth.
BTW, the sources mentioned in the other posts are reselling Guilford fabrics.