I just saw the talk about hashtag federation in the fediverse and since I havn't written anything on this topic here are my current thoughts.
I think relaying of posts, in the style of an email open relay, is probably a bad idea. It's probably a bad idea in the fediverse for the same reasons that it's usually a bad idea for email. The most obvious issue is that it easily enables spam. For example, suppose there was a hashtag for a currently urgent event. A spammer could then just flood that hashtag with ads, or a political adversary could post random garbage with the hashtag attached in order to flood out the signal with noise and make it less likely that people will pay attention to that topic.
The other issue is post integrity. Usually this is ensured by a http signature, but if a post is relayed then how do we know that the post stored on the relay is the same as the original? An evil relay could alter public posts to deliberately create flame wars and instance blocking.
So I think relaying of posts and hashtags could create more problems than they solve. In the scenario mentioned in the talk you may still get to know what's happening in a protest because people you follow will be boosting posts with the hashtag. Boosting becomes a decentralized way of distributing hashtags around between instances, without breaking the integrity checks via signatures and directly following the chain of trust from one person to another. In the relay model you need to somehow trust that the relay is not evil and it becomes too easy for bad actors to try to influence what people are thinking about a topic.