the same way it makes sense for Lemmy/Mbin/Piefed to only show posts made on a community.

To be fair, that's not how Mbin works. Its communities also capture microblog posts that weren't originally posted to a community, based on the community's configured hashtags.

This article's core argument seems to be that Pixelfed is violating the ActivityPub protocol by not displaying posts that do not contain images. That's just not true at all. I'm interested to know where the protocol ever has such a requirement.

The principle behind a communication protocol is to create trust that messages are transmitted.

And they have been transmitted. They've been filtered out after transmission, but the protocol did its job.

If a message is not delivered, the sender should be notified.

Perhaps. But that's not in the spec. There's no obligation to notify iirc that a post got filtered out on the target instance.

Even if Pixelfed sent Reject(Note) back for every post without an image, would Mastodon even display that to the user anywhere? Would most users want to see that for every post not containing an image multiplied by every Pixelfed instance it got federated to? I'd personally interpret that as spam.

Lemmy doesn't really target compatibility with Mastodon. It does have some of it by using the same federation protocol, but it's all incidential and not actually directly supported.

If you wish for proper support, I recommend switching to Mbin instead. It's a Lemmy-like project that aims to work with both Lemmy and Mastodon.

When it comes to communicating between Lemmy and Mastodon though, this is what I know:

Contacting specific Mastodon users

You can mention any Mastodon user the same way you'd mention a Lemmy user. They will get your mention and will see the post or comment you mentioned them in. Your instance doesn't need to be federating with the Mastodon instance in question for this to work, as long as you're not explicitly defederated from each other.

Federation to Mastodon

Lemmy communities show up on Mastodon as users, so Mastodon users can browse and follow them. They basically function by boosting (retweeting) every post made to them. So all you need to do for your posts to show up on Mastodon is to have a user on there follow the community you're posting in.

Posting to Lemmy from Mastodon

Mastodon users can post to Lemmy communities by mentioning them, as if they were a user. Lemmy will display them as threads despite them being microblog posts, Mbin separates Lemmy-style threads and Mastodon-style microblog posts in your feed.

Discoverability

Interacting with Lemmy communities directly isn't too common for Mastodon users, hence the low amount of contact between the two. If you want to increase your discoverability, add hashtags to your posts. Mastodon iirc mainly relies on hashtags for discoverability.

Lemmy does NOT let you browse Mastodon posts or follow users on there. Mbin does though. So again, if this is something you want, do consider switching instead.