You can now use the Azure CDN to access blobs with custom domains over HTTPS. See the following article for instructions on how to do so: https://docs.microsoft.com/en-us/azure/storage/storage-https-custom-domain-cdn. Having talked to a number of customers, we concluded that this solution addresses many scenarios where the need for HTTPS access to blobs with custom domains exists.
Native Azure Storage support for using SSL to access blobs at custom domains is still on our backlog. We would love to hear about your scenarios where using the Azure CDN is not an acceptable solution, either by posting on this thread or sending us an email at firstname.lastname@example.org.Steve Lee commented
[Can't edit my last comment] My use case is for the static web site for a AzureFunctions powered app. With Serverless set to explode this is bound to be a much wanted feature.Steve Lee commented
Glad it's on the back log. SSL is vital for all modern access, eg PWAs. and a custom domain is almost always wanted from front end access.