After a bit of time lost blaming other things I've unearthed what I think is a bug in FM 16. I took me a while to figure out so I'm sharing the workaround for your sanity.
The bug only happens on macOS and I've reported it here Base64Encode changed behaviour in 16
EDITED: I was made aware it had been already reported by another user
Basically if you use Base64Encode to create the basic auth script for a web service, FileMaker 16 adds an extra character at the end of the base 64. That makes the string "wrong" for the web service.
So if you have one such integration in 15, it will break in 16.
The workaround is to replace "Base64Encode(" with "Base64EncodeRFC ( 4648" in your scripts, but it means going through your old stuff to fix it