I have five words for you:
Christian Emergency Medical Care Providers
Explain to them that they cannot work on the day you think is inappropriate. They choose their own Sabbath, their own day for worship.
I've got another one for you:
Preachers
Are you saying they cannot work on the Sabbath?
Strawman argument Alert! Warning, Warning, Warning!!!
Luk 14:1 Now it happened, as He went into the house of one of the rulers of the Pharisees to eat bread on the Sabbath, that they watched Him closely. 2 And behold, there was a certain man before Him who had dropsy. 3 And Jesus, answering, spoke to the lawyers and Pharisees, saying, “Is it lawful to heal on the Sabbath?” 4 But they kept silent. And He took him and healed him, and let him go. 5 Then He answered them, saying, “Which of you, having a donkey or an ox that has fallen into a pit, will not immediately pull him out on the Sabbath day?”
You need to read Torah.
The impressions that you espouse are not supported therein. Your premise WRT ‘work’ on sabbath is a Takanot.