Filesystem ACLs are going to be your best solution here.
You can set a default ACL on directories, and when a file is created in that directory, it inherits the default ACL. You can then set this default ACL to allow access to the files.
For example, if you wanted to grant all users of the group
mygroup read/write access to
/var/www, you can do:
setfacl -R -m group:mygroup:rw /var/www
setfacl -R -d -m group:mygroup:rw /var/www
The first line sets the ACL on all the existing files. The second line sets the default for any new files.
And while I think it's a bad idea, if you really want to allow all users full access to the files:
setfacl -R -m other::rw /var/www
setfacl -R -d -m other::rw /var/www
Note that this will require your filesystem to be mounted with ACL support. If this is not currently the case, you can do so via
mount -o remount,acl /var/www (or whatever the mountpoint is). Then edit your
/etc/fstab and add the
acl option to the appropriate line.