What I suggest, and which mirrors practice on the (possibly quite non-representative) slice of discussion fora I have participated in over the years is:
Clearly label sensitive information. In other fora, this often involves linking your username to some real world information-- I'm thinking of old timey mailing lists, or fora where people just sign with ...
Talk to your players
Tell them that you are asking these sorts of questions and ask them to avoid looking at those while enjoying the site.
Also, follow @Novak’s advice in case the players trip over it without looking for it. As for point 1 of that answer, just tell them your username.
Ultimately, if they want to spoil their dinner, you’re not their mother.
After seeing the related Q&A on Main Meta (thanks to Rubiksmoose for finding it): Line after blockquote in spoiler not a spoiler?
I have solved the problem I was having by adding a <p> tag after the nested quote.
Specifically, what I had before (what I used in this meta question) is this:
>!This is a spoiler quote and is hidden.<blockquote&...