Just a quick note, you get to set the permissions when you create the file
So if creating lax permissions is what you want, you should be able to do that! It depends on how you're creating the file, but you can also use the fs package (or others, probably) to edit the permissions (e.g. file_chown or file_chmod) as the rstudio-connect user / owner after you create the file, if you want.
Gotta love programming languages!! 
Aside from lax permissions, the right / secure solution is as @andrie suggested - through managing user / group memberships. If everyone is a member of the same UNIX groups, you wouldn't run into this issue.