I'm conflicted about this. On one hand I agree with the idea that the best way to test whether someone can do something is to look at evidence that that can do that actual thing (i.e. write real code using best of breed tooling). On the other, a whiteboard provides a very real constraint and tests something a little less tangible than can someone copy/paste. A whiteboard test is not just a test of 'can you solve this…
And so should you. Writing sort algorithm code is a dumb thing for a software engineer to do and I don't care if you have never heard of bubble sort because it is useless historical knowledge for everyone except historians.
But you definitely should be able to make some wise suggestions about how to handle sorting of some set of data in a certain specific context.
I know there is a fad for reinventing the wheel in regard to databases these days but so few engineers will actually have to do this and so few employers will get any real value from this, that I think it is best ignored. Just consider these whiteboard interviews as a way of warning you that the potential employer probably is not such a great place to work after all.