I don't worry about most of this kind of stuff.
No one is going to care one iota about me proving I belong to a particular church in some kind of emergency.
Nor am I going to need a copy of my birth certificate or marriage license.
Government has records of who is married to who and when they were born. If those records are not accessible, you have far worse problems than the lack of a marriage license.
Medical records can be scanned, but there is no guarantee anyone on the other end will be able to use them in a practical way. It sounds like a great idea, but not many people have medical conditions that make having these kind of records available all that important. There are some people that it might matter for though. The problem is that scanned medical records are just not especially useful much of the time. For instance, you can't scan diagnostic imaging and come out with anything useful.
It might be handy to have a social security card in case you need to find work, but a scan or copy of the card is not going to do you any good.
One thing I have is my kids shot records. I read about those issues to people who left NO, school systems wanted proof of shots before allowing the kids to be registered, parents couldn't get it through to the administrators that they would have had to have all those same shots to be in the school they were in previously.