Question: Which materials obligate a garment in the mitzvah of tzitzis?
Answer: First of all, every type of material is obligated. The question is only whether the obligation is from the Torah or from the rabbis. There are two opinions:
1) One opinion holds that only garments made of all wool or all linen are obligated from the Torah. (Note: Obviously a garment made of a mixture of both is forbidden to be worn because of the prohibition of ‘sha’atnez’.) According to this view, garments made from other materials, such as cotton, silk or hair of goats, camels or rabbits are obligated only by rabbinic decree. (Note: If a garment is made of threads spun of a combination of, say, wool and cotton, it is classified under the material which constitutes the majority of its makeup.)
2) The other opinion holds that the Torah obligates garments of all materials!
Question: If either way the garment is obligated in tzitzis, of what import is it whether it is from the Torah or from the rabbis?
Answer: Probably the most significant difference is whether a person should choose to wear a garment that would enable him to fulfill a Torah mitzvah rather than a rabbinic one. Remember that nowadays, we go out of our way to buy a four-cornered garment just so that we can fulfill the mitzvah of tzitzis. So, why not choose a Torah-obligated garment?!
Question: So which opinion do we follow?
Answer: Halacha rules in accordance with the opinion that all materials are obligated by the Torah. Accordingly, a woolen garment and a cotton garment are of equal status. However, the Mishnah Berura writes that a G-d-fearing person should prefer a woolen garment to a cotton garment, in deference to the other opinion. This is the reason that many men voluntarily choose to wear a talis katan made of wool, even though the cotton ones are more comfortable. Of course, we all wear woolen talis gadols!
Question: Does it say anywhere that the tzitzis strings need to match the material of the garment?
Answer: Yes and no. Woolen strings are like the “master key” – they work on any material. (Except for on linen garments. The reason is that nowadays we are not allowed to mix wool and linen in this way.) Cotton strings would work on a cotton garment, but not on any other material. Linen strings, while technically a master-key as well, are best not to be used even on cotton garments, and are prohibited on woolen garments.