This sounds like a pretty strong argument against appointing a high-level public official to their position for life.This looks like rather a non-story to me. Don't forget it is about the 1960s, i.e. 60 years ago, when racial prejudice was still very widespread in Britain, there were relatively few members of racial minorities in the country compared to now, and there were no laws yet to curtail it. Furthermore it is about the practice of the court, rather than direct evidence of racism on the part of the monarch.
People change as the times move on. I was fairly anti-homosexual in the 1970s. Now, I'm relaxed about it, because society's norms have shifted and my views have moved with them. It's an easy game to rake over the past and find things that shock by today's standards.
I mean, it sounds like you're saying that they'll end up out of touch and ineffective eventually.
That's not the only model for a republic, but of course it would be an improvement: you can get rid of a bad head of state without executing them.As for getting rid of the Royal Family, you do realise that would mean having an elected president instead, do you? Are you sure that would be an improvement? Why?