Maybe you shouldn't make the change until you have a Selenium suite, automated rollback, blue/green deployments, a bulletproof status page, and an on-call rotation with a regularly tested runbook. Maybe we should just sit on our hands and make internal improvements until things are perfect.
Some companies value hyper-compliance, some companies value employees that speak up in cases of negligence. You have the freedom to choose your own preferences.
Furthermore, it IS possible to respectfully communicate your concerns and position without being a heroic jackass. My manager on that project and I were on good terms when I left and he served as a recommendation for my next job. The situation wasn't nearly as exaggerated as you're making it.
You then sell them the version control benefits and get them to sign off on that scope instead of being an obstructionist.
As I mentioned in another comment, I work in health now. You really can't turn a blind eye to these things in my current field. You might say I found a field more calibrated to my speed-quality balance than the old job.
Glad you're doing well and def. w health you can't move fast and go cowboy because the stakes are higher. We have clients in the health space too and the speed kind of annoys me but I've gotten used to it. But we still have clients that have used bad devs and ftp code so I see the gamut.
Personally I like the in between. Not cowboy but not corporate.