A lot of Pharisees, priests, etc. just avoided touching all women they didn’t know, so that they wouldn’t make any mistakes about their time of the month. A lot of Orthodox Jewish men still do this. (Which is why there’s a lot of Jewish folk dances that involve holding handkerchiefs instead of hands, and a lot of men-only, women-only dances.) So yup, “touch” means touch.
Women having their periods had a bit of a vacation, and they tended to hang out with other women having their periods. They already had their houses organized as a system for kosher stuff; this was just another layer of system, like a woman having her own sleeping mat for that time of the month. No big deal. Practically, it meant that guys either had to be a little bit self-sufficient at that time of the month, or they just said, “Eh, I’m unclean too.”
Frankly, a lot of Jewish guys just didn’t care, depending on their profession. The only reason Pharisees wanted to spread the more extreme, priestly rules of conduct to the ordinary people on ordinary days was that they hoped that if everybody was priest-careful to avoid ritual uncleanliness, the Messiah would come faster. (And since a lot of Judaism today is heavily influenced by Pharisaism, that explains a lot of Orthodox Jewish practices today being much harsher than anything the average Jew in Jesus’ time would have bothered to do.)
I will note that although most cultures didn’t have the exact same rules as Jewish ones, there were many many cultures around the world which believed that women either needed to avoid men, water, the fire, etc. during their periods lest dire things happen; or that women had to rest in seclusion during their periods to avoid utter exhaustion; or that women were unusually vulnerable to evil spirits at such times. So of all the things the Jews did that seemed “weird” to non-Jews, the menstruation laws were probably one of the least weird-seeming ones.
Also, remember that cleanliness and uncleanliness were not a matter of being good or bad. Contact with corpses, with leprosy, with blood,
or with sacred objects or God all made one equally unsuited for normal contact with other people. It was more about being somewhere out on the sharp edges of life than about being dirty.
So yeah, touching Jesus made you “unclean” to start out with, and thus Joseph probably didn’t worry too much.
