So whats this about not being able to reblog stuff?
What happens when I block someone from my blog?
They won't be able to follow your blog.
They won't be able to send you fan mails or asks to your blog.
They won't be able to see your blog's posts in their Dashboard.
They won't be able to like, reblog, or reply to your blog's posts.
Your blog won't show up in their search results
Basically as it was up to last week, blocking someone meant you wouldn't see posts or reblogs from blocked people, and that no one would see reblogs in the notes from that person on posts you made. So if A blocks B, and B reblogs A, A will not see the reply in their activity feed, and the reply won’t show up in under the posts notes for anyone; only people following B or going to B’s blog directly would know about the reply existing. Essentially, it let A control what replies were public to people at large; it created an echo chamber where anything A didn't like was smothered out.
The new system, rolled out last week, does all that and more. Now B flat out can’t reply at all. Previous posts still “vanish”, and you outright can’t make any new ones. It’s the ultimate “I have the last word” feature.
Look back at how ~toxic~ a lot of this site is, and how many times you wondered “why isn't anyone saying anything back?”; this is why. Look at all those posts where someone says something shockingly stupid and thankfully someone does say something; Tumblr staff is working diligently to make sure replies that upset the OP can’t happen anymore and any kind of argument the OP is losing become a thing of the past.