Can I let other people use the extension without providing my account credentials?

Yes. They will need to go to the extension setup page and login with the customer name,zone name and zone key of the zone you wish to let them access. All the zone info is available in the Zones section.
You can also use this link in order to automatically insert your guest-login credentials: 

https://brightdata.com/cp/bext?customer=YOUR_CUSTOMER_ID&zone=YOUR_ZONE&key=ZONE-KEY