Insecure document errors with media request

I’m tracking an intermittent error on iOS/macOS in Safari with trying to capture audio input using navigator.mediaDevices.getUserMedia` and I’m starting to wonder if something about the way Meteor loads dynamic modules may have something to do with it. It seems that granted permissions are invalidated by something while using the app, which causes the permission dialog to be resprung multiple times, until it eventually settles down for a while. After a hot-code push, I seem to get an error instead - no permission dialog is presented, and the system fails.

Anyone have experience with getUserMedia on iOS and macOS with Meteor in Safari?