According to the way R. Nachman Bar Yitzchok understands the Tana D'bei Rabbi Yishmael who limits בגד to garments made of wool and linen, it is in the context of the mitzvah of tzitzis. Meaning, only garments made of wool and linen are obligated in tzitzis according to the torah. However, Rava understands that the focus on wool and linen is for the strings, meaning that wool or linen strings work on any garment regardless of the material, but otherwise the strings must be the same material as the garment i.e. cottons strings won't work on a silk garment. Tosafos writes that we pasken like Rava which is the p'sak of the Rama (9:1), that all materials are obligated in tzitzis m'doraysa, but the Mechaber paskens like the tana d'bei rabbi yishmael that only wool and linen are chayev m'doraysa. Rav Moshe has an interesting teshuva where he explains that even according to the Rama, synthetic materials are exempt from tzitzis (even m'drabonon). His rationale is that only materials that require being made into threads and woven together have the status of a "beged", but materials that can be used without being made into threads such as all synthetics, even if they are made into threads and woven, they don't have status of a "beged" and are therefore exempt from tzitzis. Therefore, even if one is not going to be machmir for what the shulchan aruch considers d'oraysa, one cannot make tzitzis on a synthetic garment. A bracha recited on tzitzis when the garment is synthetic will be a bracha l'vatala.