This started when I wanted to get a "no-reply" email associated to my outbound order emails.
Step 1) I use G-Suite for my domain email. I created an Alias email under my MyName@Domain account. That alias was no-reply@Domain
Step 2) Sent test emails, both to and from no-reply@Domain. All successful using several email accounts from Yahoo and Gmail.
Step 3) In Shopify I updated "Settings" > "General" > "Store details" > "Customer Email" from to no-reply@Domain
Success) All order emails to customer started having the "sent from" address of no-reply@Domain instead of my personal email address.
This Issue: When I tested the Contact Form on my site, I did not receive the contact email to either MyName@Domain or no-reply@Domain
Attempt 1 at fixing) I tried changing "Settings" > "General" > "Store details" > "Store contact email" to no-reply@Domain and that did not resolve the issue.
Attempt 2 at fixing) I changed the email associated to my login to no-reply@Domain and that did not resolve the issue even though I received all the verification emails associated to that process to the no-reply@Domain address.