I'm normally not the person to tell you to silence anything (especially when our new way of working is about being part of a fast-reacting team), but there are some good cases to be made about silencing Chat:
When you feel overwhelmed (Chat overload is real)
When you need to focus
When you are presenting or sharing your computer with another person. Oh those colleagues with their witty GIFs
When you are out of the office.
Here are the several options you have for disabling notifications, and why some may be more appropriate than others. You can shut off everything and only silence specific conversations.
Click the big button that says "Active" and set a time when you want to be back. Chat will still change the icon colour if you have a new message, but you won't see popups. This WILL change your mobile status, too.
How to get it back: Set yourself back to active, or wait for the timer to expire.
Downside:
The icon's colour changing to indicate you have at least one unread message may cause you FOMO
You can be off for a maximum of 24 hours, this is not for holidays
Other people know when you'll be back
Android for Work users are able to disable ALL work apps at once. This will suppress all reminders (even Calendar) and save some battery (as well as the temptation to check mail).
How to get it back: Push the button again.
Downside:
Others don't see you are away
It removes ALL notifications and access. You won't be able to check your calendar, for example. Which may not be a downside at all.
Simple as that - close the tab, or the desktop app.
How to get it back: open chat.google.com in a new tab, or open the desktop app.
Downside:
others won't know you're off and suspect you are too good to reply.
You may still want to check from time to time, only not see messages.
Closing the web/desktop client doesn't impact your mobile apps.
Setting yourself to out-of-office is visible in Chat, but not recommended.
Downside:
Messages are still delivered. Alerts still play.
Chat will say you're "back tomorrow", not in one hour.
You can mute all conversations (chat rooms, group messages, 1:1 messages). See the screenshot on the left.
How to get it back: Click the conversation's meu and select Notifications. Then, select the level of notifications that you can deal with - probably No notifications.
Downside:
New messages still change Chat's icon
You need to remember to enable notifications again (if you want to)
Conversations with new messages still display in bold font.
You are entitled to leave chat rooms that are just too much. People will NOT see you left - there is no notice like when you add somebody. They will see you left when @mentioning you (it will ask "add Holger to the room?").
Note: This will work only in chat rooms, not group or 1:1 conversations.
How to get it back: Go to "browse rooms" and join the room again.
Downside:
Leaving a room might be frowned upon
It seems too much hassle to quiet a noisy room for just one afternoon.
So now if you don't answer my messages anymore, I know why! Don't worry, I'll email you. Thanks for reading!