GHCR - push inside PR fails with 403 forbidden error with GITHUB_TOKEN

Question

Having a GitHub workflow that pushes the image to ghcr. The push fails on pull-requests with 403 forbidden using GITHUB_TOKEN.

  - name: Build and push
    uses: docker/build-push-action@v2
    with:
      context: setup/docker/base
      file: setup/docker/base/Dockerfile
      platforms: linux/amd64
      push: ${{ steps.docker-vars.outputs.has-docker-secret == 'true' }}
      tags: ${{ steps.docker-vars.outputs.tags }}

The permission are set to "write", is there a way to fix it or to let them push to their own ghcr url in pull-request?

The step should not be skipped.