I think most Americans would be fine with it. Hospitals, the military, and most public services like fire fighters use it already.
E.g. despite abortion clinics having a history of being violently attacked and often "regulated" out of existence, only roughly 20% of Americans think abortion should be flatly illegal outright and the labels "pro-life" and "pro-choice" seem to be self-applied in roughly equal proportions:
https://news.gallup.com/poll/1576/abortion.aspx
Granted, abortion is a complex and sensitive topic even before you bring religious doctrines into it, but it only takes one snowflake with a gun to think changing the clocks is Satanism for someone to get hurt. I'm frankly amazed the DST change seems to have passed so easily given the kind of conspiracy theories that would lend itself to.