There's a thread on the forums that's been highly active over the last few days that I find deeply disturbing. Is there a way that I can block it from showing up under "Recent Posts" or block/ignore posts by the member who posted it?

there isn't a feature to ignore threads, but users can be set to ignore via the "Personal Messaging" part of your profile (don't ask me why it's there, i don't know)

Thank you.

Nope, sorry.
Just don't click on it.

The problem is that I find the title itself more than a little disturbing, and each time I see it it reminds me of the content of the post.

hope it dies down quickly?

You can set the board on ignore if it's a place you don't frequent.