Summary of investigation
I've updated my /etc/hosts to force tracker2.wikimedia.cz to go to 127.0.0.1. I've then configured my localhost Apache to act as a reverse proxy and forward all traffic going to tracker2.wikimedia.cz to localhost:8000 (that's where the development instance of Tracker is running). This was done to be able to use real tracker2.wikimedia.cz OAuth consumer to debug the issue in localhost environment. I've then changed OAuth consumer tokens in settings.py to 99be4b77991ee5e7f2fc034387aead3e (the tracker2.wikimedia.cz consumer). The issue persisted. However, when I changed the tokens back to the localhost one, the issue no longer appeared.
Original task description
See https://ctrlv.tv/SAAy. This is happening only on production, not with localhost tokens.