Issue the following command in your Acme repo. It adds a new remote repository named upstream that points to the Generic repo.
git remote add upstream https://location/of/generic.git
You can then merge any changes made to Generic into the current branch in Acme with the following command:
git pull upstream
If you just want it to download the changes without automatically merging, use git fetch instead of git pull.
If you want to disable pushing to that repository, set the push URL to an invalid URL using something like
git config remote.upstream.pushurl "NEVER GONNA GIVE YOU UP"
Git will now yell at you about not being able to find a repo if you try to push to upstream (and sorry about the Rickroll, but it was the first random string that popped into my head).