Unable to join room via matrix: 403 Forbidden reponse to make_join

When trying to join #fish-shell_fish-shell:gitter.im via Matrix (alias obtained by clicking on the "Chat via Matrix" button on https://gitter.im/fish-shell/fish-shell), gitter.im response to the make_join request with a 403 Forbidden:

Feb 05 09:15:07 matrix synapse[350]: synapse.http.matrixfederationclient: [POST-6941681] {GET-O-13216399} [gitter.im] Completed request: 200 OK in 0.10 secs, got 492 bytes - GET matrix://gitter.im/_matrix/federation/v1/query/directory?room_alias=%23fish-shell_fish-shell%3Agitter.im
Feb 05 09:15:07 matrix synapse[350]: synapse.http.matrixfederationclient: [POST-6941681] {GET-O-13216400} [gitter.im] Got response headers: 403 Forbidden
Feb 05 09:15:07 matrix synapse[350]: synapse.http.matrixfederationclient: [POST-6941681] {GET-O-13216400} [gitter.im] Request failed: GET matrix://gitter.im/_matrix/federation/v1/make_join/%21YLTeaulxSDauOOxBoR%3Amatrix.org/%40xiretza%3Axiretza.xyz?ver=1&ver=2&ver=3&ver=4&ver=5&ver=6&ver=org.matrix.msc2176&ver=7&ver=8&ver=9&ver=org.matrix.msc3787&ver=10&ver=org.matrix.msc2716v4: HttpResponseException('403: Forbidden')

The same thing also happens for users on matrix.org.