That's a bit of a spun story. There was apartheid proper, and technically apartheid. By that time, '86, my colonial school had black students. Tutu didn't need exemption, and wasn't being particularly rebellious.
https://en.wikipedia.org/wiki/1986_in_South_Africa it's a litany of explosions and killings, and the turnaround may have been in the works, but it doesn't surface until December '88 when "Nelson Mandela is moved to Victor Verster Prison" (from Robben Island)
I don't recall school in integration in '86 near me and yes, I would have noticed. If you had that you were lucky.
I wasn't assuming that Mr Tutu was taking any great personal risk, but he was driving progress with cheerful good humour.