Is it a bug from Shopify?
We are having the same problem (but with Local Delivery). I chatted with a Shopify Employee and they told me that it is currently not possible to remove shipping costs with Apple and Google Pay. For us, sadly, this makes these checkout options unusable since most of our customers are mobile users...
A feature request has been sent in to Shopify but I have no idea how long it will take before this feature will see the light of day.
Have a good one!
Jordi from Drinkz.nl
I will also mention that I have been refunding people shipping charges left and right and finally realized there is a problem using Apple Pay and Google Pay for free local delivery or free shipping. As stated here, charges automatically apply when using these methods. I will have to turn them off for now. Hoping for a quicker resolution to this glitch.