No, it must be something else. I can’t see them no matter what browser I use.
It seems to be Theme-specific. All the emojis show up in “Discourse Classic”, while “Sam’s Theme” and at least one other only shows the emojis for the parts of a post inside of quotes. That’s some half-assed theming they’ve got going.
All right. Let me check again.
I added the emoji after changing the theme; therefore, the presence or absence of emoji is theme specific, I can confirm this now.
And I want to mention that it didn’t allow me to edit the post to add this information - it said that the post was too old to be edited.
Testing the emojis.
They seem to be working on Simple Sam.
Simple Sam is the one I’m using now.
Nothing.
Using Simple Sam I could not see your emojis, @cochrane unless I quoted you. I just switched from Simple Sam to Discourse Classic and I can see everyone’s emojis again. I think.
Yes, that is what I had to do as well earlier.
I see them all, including in this post. I am using Discourse Classic in the Safari web browser on my computer.
I’m using the Vincent theme right now, and I can see them all - it is a theme related feature.
Wait, let me check:
Is there any emoji showing?
ETA: no, there isn’t. hmmm… they only show when they’re quoted.
I am using Discourse Classic and I can see unquoted emojis. 
Well, I’m using the default theme and, when I click “reply”, there is a tool bar above the space where you key in your reply. On that tool bar is a round smiley face. When I click it, a LARGE menu of many emojis opens up. All I know is that it is there for me.
They are there in every theme, only they don’t show when posted unless you use the right theme.
Which is … ?
Take a look at what this guy here says:
Thank you!
Funny. I’m using Sam’s Simple theme and I can see my emojis and everyone else’s and I don’t have to quote anyone. I wonder if it’s because I’m using a phone and some of you are using PCs.
When I change my user-agent to Chrome on iPhone, I see the emojis, too. Using the Light theme.
BUT it takes the avatars out of the quoted posts…
ETA: Avatars seem to be out of quoted posts on every setting.
I am using Sam’s on my laptop.
ETA: I can click on the emojis but they don’t actually show up when I view them.