@felix Mastodon sends this:

Accept: application/activity+json, application/ld+json; profile="https://www.w3.org/ns/activitystreams", text/html;q=0.1

This also returns HTML. application/activity+json by itself works. Many web frameworks parse the Accept header and allow specifying different handlers for different content types. I only had to specify it twice to cover all possible cases:
https://github.com/grishka/Smithereen/blob/master/src/main/java/smithereen/Main.java#L192