Constitutional guarantees are in "tension" with each other. (That's the phrase I've heard lawyer-type people use.)
The Constitution also says that Congress can regulate interstate commerce, Article I, Section 8, Clause 3. Eg, in Heart of Atlanta Motel v. United States, the Court decided that the motel's racial discrimination hinders interstate travel, and thus under the Commerce Clause was required to follow Title II of the Civil Rights Act of 1964, despite the motel's owner arguing (among others) "that it violated his Fifth Amendment rights to choose customers and operate his business as he wished." https://en.wikipedia.org/wiki/Heart_of_Atlanta_Motel,_Inc._v...
This is all well-established law over the last 60 years. And with 60 years of people working to tear it down, which appears to be what's happening here.
Further, if you voluntarily take federal money (as almost all schools do) then you must follow federal rules, like Title IX of the Education Amendments of 1972 which prohibits sex-based discrimination in schools. This Hawaiian school does not take federal money so avoids those laws.