How to use with branch protection?

We have tried enabling this action in https://github.com/kubernetes-sigs/descheduler (see https://github.com/kubernetes-sigs/descheduler/pull/298), but run into the problem that `gh-pages` has branch protection enabled (to verify the linuxfoundation CLA check).

This check is required for [all Kubernetes repositories](https://github.com/kubernetes/test-infra/blob/8caafb254d5fcc15707af17ede14ccb761f7a878/config/prow/config.yaml#L112-L117). Other projects have also hit this problem (https://github.com/kubernetes/autoscaler/pull/3393#issuecomment-668081392). As shown in that comment, this can be addressed by using 3rd party chart-releaser actions and taking steps like having them open PRs.

However given that this is the official chart-releaser action it should be usable by Kubernetes projects rather than having to rely on 3rd party scripts. Is there a way to configure this to work with branch protection?

If not, I believe one fix would be to update this action to optionally decouple the actual Git push (which is baked into the action) so that it can be replaced with a more configurable Pull Request action (like here, which is using a 3rd party action: https://github.com/kubernetes/dashboard/pull/5311/files#diff-29eba779142f216406df01a921ea49c3R59-R66)

Review the action's current Git push behavior and branch-protection requirements, using the linked descheduler pull request and Kubernetes examples as context. Determine whether configuration can support a protected gh-pages branch or whether publishing must be decoupled into a pull request workflow; done means a documented, tested path for Kubernetes repositories.

Written by the indexing model from the issue text.