Thinking about buying Executive tools, but not sure the best way to listen while driving.
Do I need to open the website and play the logged in pocast from the webpage?
Or is there a CarPlay freindly player that can play the logged-in Executive Tools podcasts?

Access via the stock "Podcasts" app
Just for grins, I just tried via my iPhone's stock "Podcasts" app -- successfully. That iPhone plays podcasts from that app seamlessly through CarPlay in my commute car.
I still find Executive Tools too engrossing to be background material! So I listen to Executive Tools through my MacBook's Podcasts app, where I can keep it as primary focus, take notes, and pull up show-notes as I wish.
Overcast
My favorite podcast player is Overcast, available for iOS. It has great carplay integration, and can syncronize subscription-pased podcasts like Executive Tools. It has features that the normal podcasts app doesn't, like smart speed, which cuts out silence, and some other audio-based improvements unique to this app.
If just listening to this one podcast, the built-in podcast app jrb3 listed should be fine.