There is a prohibition stated in the Torah that a person can't wear a garment that has both wool & linen in it. This law is called 'Shatnez'. Do all denominations of Judaism follow this law? If so, how is it observed? If not, why is it not observed?

The Torah commands us not to wear shatnez, a garment that contains both wool and linen in the same garment.  See Vayikra (Leviticus) 19:19 and D’varim (Deuteronomy) 22:11.  Orthodox Jews regard this Torah law very seriously, even today in modern times.  When we buy garments, we “read the ingredients,” just as we do with food, to assure initially that the clothing is not linsey-woolsey.  Although we typically trust the labels for shirts and blouses, pants, dresses, undergarments, all-silk ties, etc., we are more concerned about garments like men’s sport coats (“sport jackets”) because many of them include unlisted fabrics in the inner linings and paddings, particularly in the inner collar.  So, for example, a labeled “100% all-wool suit” might have linen material to stiffen the inside of the collar or in the padding in the shoulders. Or an all-linen sport coat may have wool felt in its padding. A lady’s all-wool garment may have linen in a sewed-on design or appliqué.  Therefore, when buying a garment of that sort, we ask the store to have it tested first for shatnez.  If the store does not provide the service of sending garments out for testing, we need either to buy from a different store that does or to figure out an alternative way to have it shatnez-tested before finalizing our purchase.  Indeed, certain suit makers are known always to use linen in the paddings or collar linings of their wool suits, and we therefore are aware from the outset not to bother looking at their lines of clothes, just as we do not even bother to read the ingredients of Oscar Mayer cold cuts.

 

So the Torah laws of shatnez certainly are still very observed.  Modern-day shatnez-testing includes taking a small portion of the padding or lining from a section no one will notice, and looking at the fibers under a microscope.  The differences among fabrics like wool, linen, and other natural and artificial fibers that appear under a microscope are striking, easily detectable.

 

We may wear an all-wool coat over an all-linen shirt, or vice-versa.  The Torah prohibition bars only the mixture within a single garment. But within that garment, even the most minuscule mixture is forbidden.  Shulchan Arukh Yoreh Deah 299.  Even if the only linen in the all-wool garment is the thread used by the manufacturer for sewing in the label, it is forbidden shatnez.  See, e.g., Rambam, Mishneh Torah, Hilkhot Kil’ayim 10:5.  By contrast, there is no concern that two separate garments, one linen and one wool, may touch.  We are concerned about linen only from flax but not from any other source, and only about wool from lambs or sheep, not from camel’s hair, alpaca, or any other animal.

 

Many garments can be repaired from being shatnez.  The linen collar lining in the all-wool suit often can be replaced.  The wool felt padding in the linen garment often can be replaced.  The linen thread that sewed the label into the all-wool coat also can be replaced.  The cost of shatnez-testing is very nominal, only a few dollars, and it assures the wearer that he or she is observing an important Torah law assigned to us by G-d. 

Very few Reform Jews observe the mitzvah of shatnez, but it cannot be said that Reform Judaism as a “denomination” does not “follow this law.” In fact, it seems worth remarking at this point that “denominations” of Judaism do not “follow” or, for that matter, not “follow laws,” at all. Individual Jews (of every stripe) do (or do not).

 

Your question suggests that the different streams of Judaism define themselves primarily in relation to the their adherents’ observance of traditional Jewish law. I’d like to suggest that, rather, the various streams of Judaism are differentiated according to how they characterize the relationships between God, Torah, and Israel. 

 

Orthodox Judaism recognizes Torah as the word of God, from Sinai. From this unswerving understanding of Torah, the rabbis and Rebbes of various traditional Jewish communities interpret and apply halakhah, Jewish law.

 

Reform Judaism recognizes Torah as the sacred literary fruit of any number of human thinkers, struggling to understand God, and to divine what God would say about the creation of the world, the role of human beings within the world, and proper human conduct within that role. Reform Judaism sees revelation as an ongoing process, one in which every informed, educated Jew may participate and, in fact, must participate. Because the origin of the halakhic system rests on a divine-human collaboration, each of us, according to Reform Judaism, has the authority to interpret and observe the traditional mitzvot as we see fit.

 

The halakhah of Reform Judaism (along with many progressive Jews,  “denominationally” affiliated or not) prioritizes the ethical imperative of the prophetic tradition above strict adherence to traditional and ritual halakhah, and furthermore suggests that ritual practice should bring meaning, relevance, and spiritual edification.  Some progressive Jews consider reason, as defined by the scientific method, to be a top priority in determining religious practice.

 

Thus, some Reform Jews may not observe shatnez because it is categorically an inexplicable mitzvah, or chok, and its observance is, by definition, irrational. Others (since many of us do not require our religion to be entirely rational) may, in the words of Franz Rosenzweig, “not yet” observe this mitzvah. Others choose not to because we have not (yet?) found that it elevates our spirit or deepens our relationship with God or Judaism. Some Jews, Reform and otherwise, of course, do not observe shatnez because they have never learned of it. Jewish education and familiarity with the tradition (especially in the case of Reform Judaism, which emphasized the importance of informed choice as regards traditional observance, and which values secular culture and education alongside our Jewish heritage), is simultaneously a very high value and a challenge to our community.