Example toot : https://mstdn.io/@angristan/476554
From my instance :

From his :

And the emoji does not even show up in the HTML :

It's not a problem with CSP, and it happens since 1.2.
As you can see in my example toot, it happens with some instances, but not all.
master (If you're a user, don't worry about this).I confirme.
Another example:
From my instance:

And from his:

And same, no emoji in the HTML:

It affects also the "internal" stream.
As mentioned above, emojis aren't in the HTML content, I've also checked and it's not even returned by the API (see screenshot):
export USER_AGENT="Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:45.0) Gecko/20100101 Firefox/45.0" TOKEN=YOUR_TOKEN
curl -s -X 'GET' \
-H "User-Agent: ${USER_AGENT}" \
-H "Authorization: Bearer ${TOKEN}" \
--url 'https://mastodon.xyz/api/v1/statuses/900842' | python -c "import sys, json; print(json.dumps(json.load(sys.stdin), indent=4))"

I think this might have been solved by #1988鈥攃an someone confirm?
I'm on latest code. You can try here : https://social.targaryen.house/@wonderfall/809705
And switch between instances. It seems emojis are sent and are in the HTML content, but other instances can't do that. However, someone on 1.2 managed to send me some, and they are displaying on my instance, but not totally. Check the link.
Should be fixed now.
Most helpful comment
As mentioned above, emojis aren't in the HTML content, I've also checked and it's not even returned by the API (see screenshot):