This is with default values, a brand new, otherwise empty minikube. I suspect something is broken?
fyi, I tried rolling back to Kubernetes v1.12.3 and I get the same error outcome.
~ minikube delete
Deleting local Kubernetes cluster...
Machine deleted.
~ rm -rf ~/.helm
~ minikube start --memory 8000 --kubernetes-version v1.13.0
Starting local Kubernetes v1.13.0 cluster...
Starting VM...
Getting VM IP address...
Moving files into cluster...
Setting up certs...
Connecting to cluster...
Setting up kubeconfig...
Starting cluster components...
Kubectl is now configured to use the cluster.
Loading cached images from config file.
~ eval $(minikube docker-env)
~ helm init
helm init
Creating /Users/myname/.helm
Creating /Users/myname/.helm/repository
Creating /Users/myname/.helm/repository/cache
Creating /Users/myname/.helm/repository/local
Creating /Users/myname/.helm/plugins
Creating /Users/myname/.helm/starters
Creating /Users/myname/.helm/cache/archive
Creating /Users/myname/.helm/repository/repositories.yaml
Adding stable repo with URL: https://kubernetes-charts.storage.googleapis.com
Adding local repo with URL: http://127.0.0.1:8879/charts
$HELM_HOME has been configured at /Users/myname/.helm.
Tiller (the Helm server-side component) has been installed into your Kubernetes Cluster.
Please note: by default, Tiller is deployed with an insecure 'allow unauthenticated users' policy.
To prevent this, run `helm init` with the --tiller-tls-verify flag.
For more information on securing your installation see: https://docs.helm.sh/using_helm/#securing-your-helm-installation
Happy Helming!
~ helm repo update
Hang tight while we grab the latest from your chart repositories...
...Skip local chart repository
...Successfully got an update from the "stable" chart repository
Update Complete. ⎈ Happy Helming!⎈
~ helm install --name myprometheus stable/prometheus-operator
Error: release myprometheus failed: customresourcedefinitions.apiextensions.k8s.io "alertmanagers.monitoring.coreos.com" already exists
I rolled back from helm 2.12.0 to 2.11.0 and the error went away and prometheus-operator resumed working. There appears to be some incompatibility between the new Helm 2.12.0 and prometheus-operator. I presume that will get resolved in time.