The US Supreme Court ruled (twice) that the Little Sisters of the Poor could not be compelled to pay for abortions as part of their health care plan and state officials (in Florida) forced them back to court. Even after Trump obtained legal protection for the Little Sisters in 2018, several states sued to challenge the exemptions for the nuns.
To have a religious exemption, you first and foremost have to live in a country that gives any credence to religion. (If you live here in the United States, then you don't live in such a country.)
Is it possible that a religious exemption may be granted? Perhaps. But if history is any guide, it will only be temporary; the political persecution will almost certainly become a religious one.
Interestingly, many of the most lopsided U.S. Supreme Court decisions in recent history have been those that have upheld religious protections of various kinds. It’s not unusual to see these end up as 8-1 or 9-0 decisions. This is why the Amish are exempt from Social Security and compulsory education laws, Native Americans can smoke illegal narcotics in their tribal ceremonies, and Jehovahs Witnesses and Quakers are exempt from the military draft.
There will be no religious persecution as long as two particular groups refuse to get vaccinated:
1. Muslims
2. Orthodox Jews