How can I use a buildah script for image generation using GitHub Actions?
Here is what I did, I create a Makefile that includes my own method of image creation,
.PHONY: image clean image-release
image: image-release

image-release:
    cargo build --release
    buildah unshare ./image/distroless.sh release

clean:
    cargo -v clean

For this purpose the only thing that matters is the image created by ./image/distroless.sh matches the action (redhat-actions/push-to-registry) in the following flow. We'll continue using the name myAlpineImage as in the question,
name: Distroless Image Creation

on:
  push:
    branches: [ master ]
  pull_request:
    branches: [ master ]

env:
  CARGO_TERM_COLOR: always

jobs:
  build:

    runs-on: ubuntu-latest

    steps:
    - uses: actions/checkout@v2
    - name: Download and create image.
      run: make image-release
    - name: Push To Registry
      uses: redhat-actions/push-to-registry@v2.1.1
      with:
        image: myAlpineImage
        tags: latest
        registry: ghcr.io/evancarroll/project
        username: evancarroll
        password: ${{ secrets.GHCR_TOKEN }}

You can see here we make the call to make image-release which calls the buildah script and makes the image rootless.
Then I added the secret for GHCR_TOKEN to my repo. The token is generated in the &quot;Settings / Developer settings / Personal access&quot; tokens on github..