Everybody is piling in with their opinions on this story. From an economics/accounting stand point, those schools are stupid for turning down the bequests, which were earmarked for paying for school places for "poor white boys".
Perhaps Bryan Thwaites did this for entirely benevolent and altruistic reasons; perhaps he was a downright racist - that is entirely irrelevant.
The point is that such schools usually award a few free places anyway to maintain the pretense that they are charitable institutions, which secures them a very modest corporation tax break and a very hefty Business Rates discount (which will be phased out in Scotland next year). Ultimately, the reason for this is to bump up their grade averages, thus attracting more fee-paying pupils, it's like a loss leader.
We would assume - or hope - that some of those free places would have gone to "poor white boys" anyway, so all the schools have to do is to match the income with the corresponding largely notional expense.
Let's say that in the absence of the bequest, they would have handed out ten free places, five to "poor white boys" and five to "poor non-white boys". The bequest pays for, say, two free places, they just earmark two of them as "Thwaites Scholarships" and reduce the number of other free places awarded to "poor white boys" from five to three; thus maintaining the intended five/five ratio (and banking the bequest for themselves).
If they want to be politically correct and pass on the benefit of the bequest, then in addition to the two "Thwaites Scholarships", they could also award the planned ten free places off their own bat, four to "poor white boys" and six to "poor non-white boys", meaning that instead of five/five it's six/six and everybody wins, including at least one "poor non-white boy".
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To give another example, I vaguely remember a case where a non-white person was prepared to be an organ donor, but insisted that his organs could only go to a non-white person (or perhaps it was the other way round, doesn't matter). The NHS turned him down for being racist.
Equally stupid.
If you are white and on a waiting list for a new heart, the chances are there are some non-white people ahead of you on the list. You aren't going to get that non-white heart, but a non-white person above you on the list will, so at least you move up the list and benefit from the donation, however indirectly.
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