Can one get their head hair cut by someone of the opposite gender? Is the unavoidable proximity and contact problematic?
Assume no issue of seclusion applies. I'm asking about the issue of proximity and contact only.
According to dinonline and their sources below, "it is not permitted for a man to receive a haircut from a woman. Because the need for a haircut is not considered a state of “illness”, and because the close contact with a woman is liable to cause the man hirhurim, a long list of authorities has written that it is prohibited."
Sources: Yalkut Yosef (EvenHa’Ezer 21:5); Rivevos Efraim (5:507); Hilel Omer (Even He’Ezer 38, p. 400); Yitzchak Yeranen (vol. II, Even Ha’Ezer 1); Olam Yitzchak (2:237); Netzach Yosef (1:66); Mitzvos Ha-Nashim (35:12, and sources no. 14).