I've had zero issues connecting PowerBI to a Mendix OData source to be honest. Are you sure you are using the correct credentials?
That's exactly what I did Jonathan. See below
1. Add Data source
2. Choose Odata
3. Enter your correct URL (for me this is: https://myapp.mendixcloudcom/odata/ALG (where ALG is my ODATA source in Mendix)
4. Enter your basic authentication credentials (your Mendix user + password with sufficient rights)
In the next screen you should see all your OData resources for that feed:
You can select the ones you need and continue on
In my case I want to connect power bi to the published application data, not to the localhost. It's possible?