If a bursary or service is offered to a specific group of people it will automatically exclude those who fall outside of that group. The provider needs to specify where the group boundary is. There probably also needs to be a decent reason to offer to that group at the exclusion of others. Wherever you draw the boundary with whatever group there are always going to be people who feel excluded or upset to be the "wrong" side of it. But there's always going to be a boundary unless your resources are infinite. If the theatre fund was for anyone then the self selecting groups to benefit would be the loudest /most organised /pushiest/most confident /most time to spare to search for funding etc which would in a way be a boundary excluding those who don't have those qualities.
I guess in this instance they've drawn the boundary not at actual race or heritage but reported experience. He's clearly a very confident man to have pulled this off. I'm a very white person with a foreign name who has experienced discrimination in job applications because of my name. I can't imagine trying to equate that with a lived experience of being black though. Part of white privilege, I think, is not even realising all the ways in which I have that privilege.
Ironically sex is probably the easiest and most scientifically provable way to group people. Grouping people by gender a la girl guides and co is really quite weird if you think about it, especially as there's so much disagreement about what gender is, whether it is chosen, imposed or innate and how many genders there are.