No Access to Community Content Library

Have you tried:

1. Do you have Online Access Turned On, in the Games Options?
Go to: Options - Game Options - Other

2. Turn off Origin In-Game:
Open Origin, Select Origin > Application Settings > Origin In Game tab and click the on/off switch to disable Origin In Game. - This deactivates Origin In-Game, as it has been known to cause problems with games.

3. Right-clicking the shortcut and 'Run as Administrator'

4. Go offline with Origin. Completely exit Origin and Sims 4. Start Origin and the game again and select Go Online.

*If exiting Origin isn't working, open Task manager (Ctrl-Shift-Esc) search for a file called TS4.exe or Origin. Click on it and select end process.

5. A Sims 4 factory reset:

Resetting the game to factory settings without reinstalling
https://answers.ea.com/t5/Technical-Issues-PC/READ-FIRST-Troubleshooting-your-Game/m-p/3621199#Resetting

6. Do you have an underage account (Under 14)? There are some Origin age restrictions. They are setup to be parentally supervised.
https://help.ea.com/en-us/help/account/aging-up-an-origin-account-to-an-adult-account/

7. It may also be your firewall or other malware programs, check those:
https://answers.ea.com/t5/Technical-Issues-PC/READ-FIRST-Troubleshooting-your-Game/m-p/3621231#Firewall

8: A Check List at Carl's Sims 4 Guide
http://www.carls-sims-4-guide.com/forum/index.php?topic=22709.0

9. There was maintenance on Thurs. May 10th 2018, but EA_Mai said it was done within the 3-4 hour time frame that she talked about.

The Sims 4 Maintenance - May 10th, 2018

https://answers.ea.com/t5/Technical-Issues-PC/The-Sims-4-Maintenance-May-10th-2018/m-p/6790767#M1135

If you are still having issues connecting to the community gallery, you might try posting in the thread linked above to see if she or someone else maybe of help.

(Thank you @Sashas0nic for the added tips)