Question: Is there a preference to wearing woollen tzitzis? Am I allowed to remove my tzitzis if I’m hot in the summer?
Answer: While according to the Torah one only needs to place tzitzis on a four cornered garment if one wears one, the Gemara (Menachos 41a) writes that should wear them at all times. The poskim (Aruch Hashulchan OC 8:2; Yechaveh Daas 4:2) write that it has become the accepted custom to wear tzitzis (on a tallis katan) throughout the day. R’ Moshe Feinstein (Igros Moshe OC 4:4) emphasises its importance, writing that it now forms part of the mesorah and R’ Binyamin Zilber (Az Nidberu 2:55) argues that wearing tzitzis is part of the actual mitzva.
There is a machlokes between the Shulchan Aruch (OC 9:1) and Rema as to whether non woollen (or linen) garments are obligated to have tzitzis attached mideoraisa. As sefardim generally follow the Shulchan Aruch, R’ Ovadia Yosef (Yalkut Yosef 9:1) writes that one should try their utmost to wear woollen tzitzis even when it’s hot. While ashkenazim generally follow the Rema who writes that the mitzva applies to all materials, the Mishna Berura (9:5) writes that it is best to wear woollen tzitzis (See Halichos Shlomo, Tefilla 3:25). R’ Moshe Feinstein (Igros Moshe OC 2:1) writes that one who is uncomfortable wearing woollen tzitzis in the heat, can rely on the Rema and wear a cotton pair.
Nonetheless, it is reported that both the Vilna Gaon (Maaseh Rav: Birchos Hashachar 17) and the Chazon Ish (Shoneh Halachos 9:1) wore non-wool tzitzis (See Teshuvos Vehanhagos 1:18).
While R’ Zvi Pesach Frank (Har Tzvi 1:9) writes that garments made from synthetic materials such as polyester require tzitzis, R’ Moshe Feinstein (Igros Moshe OC 2:1) writes that they don’t (like leather). Thus, R’ Eliezer Waldenberg (Tzitz Eliezer 12:3) writes that one shouldn’t make a beracha over wearing such a pair.
R’ Binyamin Zilber (Az Nidberu 2:55) writes that one must wear tzitzis even while playing sports (See Piskei Teshuvos 24:1).
R’ Ephraim Greenblatt (Rivevos Ephraim 4:15) questions whether it is appropriate to wear them directly on one’s skin like an undergarment. Elsewhere (Rivevos Ephraim 7:265), he writes that R’ Yosef Shalom Elyashiv allowed people to remove their tzitzis on a particularly hot day (See Tzitz Eliezer 14:49:2).
In conclusion, many hold that there is a preference to wearing woollen tzitzis. One should wear tzitzis at all times under normal circumstances, only removing them if they are causing distress.