Should the employees be taking the rolling garbage can from behind the counter and all of the boxes for recycling out the front door?

Starbucks... It's not like you're at the freaking Ritz-Carlton.

It has a back door.

The only doors are at the front so this is ok. Every Starbucks has employees taking trash out where people can see it

Wow

If there is a back door, and it allows access to the garbage bins, then no. Next time you are there, look around the building to see if there is a back door, and if so, talk with a manager about it