Is there a way to block someone so they can not see your posts? OR we see theirs?

 

No, there is no way you can block someone from seeing your own posts. That's especially true given the content is publicly viewable.

You can put a member on your Ignore list, using the option in the UserCP, and their posts will not display to you while you're logged into your account. However, it's possible if their post is quoted that you may see their original post. This also blocks PM exchanges.