I am very confused. I had thought that the idea that a Jewish man may not touch a niddah, any niddah, except for perhaps his first-degree relatives, was basic information. Now, someone very knowledgeable has told me that this prohibition is not so; that the rules against touching not-one's-wife are only -- ok, "only" -- from the idea that one thing could lead to another.
This distinction seems like it could make a huge practical difference, for example, with handshaking in a case of significant need, or with jostling people on a bus, and other touch that is clearly (CYLOR) non-affectionate.
So what is the real reason for the prohibition for a Jewish man to touch a woman other than his wife: a pure prohibition on touching any niddah, or as a fence against relations (or against "affectionate touch" of a niddah, which it seems is also prohibited)?
Evidence that it's niddah:
The stringencies on chuppat niddah. Although I guess there's a question of at what point the woman is considered married, to me this is good evidence, because the chances that they'd transgress under the chuppah are pretty close to zero. (But maybe, on the other hand, it could be evidence that we obey rabbinical prohibitions even if their motive no longer exists. [But then couldn't the rabbis relax their prohibition for the occasion, especially in view of the embarrassment to the bride?])
Much of the layman's Internet, including this article, which states:
The second of these verses [...] [“Do not come near a woman during her period of uncleanness to uncover her nakedness” (Leviticus 18:19)], applies not just to one’s wife but to any other women as well, married or not (Responsa Rivash 425, Lev. 18:19). The rabbis extend this prohibition to include not just sex, but all touching. And since unmarried women do not go to the mikveh, they are considered to be always in a state of niddah –and therefore always off-limits for sex, or physical contact with men.
But from the same article:
Evidence that it's not niddah:
Maimonides and Nahmanides, in a well-known rabbinic debate, consider how serious an infraction it is to touch a woman who is a niddah. According to Maimonides in Sefer Hamitzvot, “whoever touches a woman in niddah with affection or desire, even if the act falls short of intercourse, violates a negative Torah commandment” (Lev. 18:6,30). Yet Nahmanides’ (1194-1270) commentary states that acts such as hugging and kissing do not violate a negative commandment of the Torah, but only a rabbinic prohibition.
The Siftei Kohen (17th century) further explains Maimonides by stating that he was only referring to hugging and kissing associated with intercourse. There are several places in the Talmud that the Amoraim (talmudic rabbis) hug and kiss their daughters (Kiddushin 81b) and sisters (Shabbat 13a), and their behavior is considered permissible.
This answer: https://judaism.stackexchange.com/a/71543/1516
The idea that harchakos are still stricter with one's wife
The idea that many distinguished poskim permit strictly non-affectionate touch such as the handshake and jostling mentioned.