Is it possible to share a particular resource (redis cache in my case) across multiple resource group?
Your redis cache could be used from any code you write, whether in the cloud, on-premises, or wherever, given proper uri + access key.
As long as you have access keys/passwords/etc. to your resources, you can use your resources no matter what resource group they're in. This includes ssh keys, vm usernames/passwords, redis cache keys, storage keys, cosmos db keys, sql database logins, etc.
The only thing access-specific, with resource groups, is granted user permissions. That is: if you add someone as a contributor to resource group A, and not to resource group B, they won't be able to manipulate the settings in resource group B via the portal or any of the Management APIs. Still, they'd be able to work with all of the resources in resource group B, assuming they had the login details / keys / etc.