But you've unfortunately given a misleading impression of Title IX by overlooking an important part of the regulations you've quoted and focusing solely on the parts that mention contact sports.
The section of the Title IX regulations you've quoted was written in the 1970s and has been in place ever since then. It says that educational insitutions which are recipients of federal funds
"may operate or sponsor separate teams for members of each sex
where selection for such teams is based upon competitive skill
or
the activity involved is a contact sport."
Moreover, the part of the Title IX regulations that gives examples of contact sports isn't about the issue of whether the federal statute allows for covered schools in the US to offer and operate separate sports teams for the two sexes in the first place. Rather, it's expressly dealing with the issue of whether and when Title IX allows students of one sex to try out for a school sports team of the opposite sex.
The regulations stipulate that where a school or other educational program which is a recipient of federal funds
operates or sponsors a team in a particular sport for members of one sex but operates or sponsors no such team for members of the other sex, and athletic opportunities for members of that sex have previously been limited, members of the excluded sex must be allowed to try-out for the team offered unless the sport involved is a contact sport.
For the purposes of this part, contact sports include boxing, wrestling, rugby, ice hockey, football, basketball and other sports the purpose or major activity of which involves bodily contact.
The section about students of one sex trying out for teams of the opposite sex in this section of the Title IX regulations written in the 1970s is really about female students trying out for boys' and men's school sports teams. Because historically, athletic opportunities in publicly-funded US education were limited only for members of the female sex.