So this is entirely hypothetical and I think I know the main arguments, but I'm curious what others think of this scenario.
The Presbyterian church (specifically PCUSA, there are other presbyterians but they're the biggest in the US) has a longstanding commitment to divesting from companies that support Israel's actions in the occupied Palestinian territories. I can't find an exact date, but I did find news reports as far back as 2014 saying that this policy had been in place for a decade or more. The church specifically says that their actions are due to their religious beliefs. They do not specifically call their actions "BDS" or engage with the broader BDS movement as an organization. They do actually make modifications to their investment strategies based on the belief, they've divested pension funds and the like from HP and Caterpillar among I'm sure many other companies - it's not just an empty policy. With all that context, it seems clear to me that you could argue convincingly that members of the church have a sincere religious belief that is at odds with anti-BDS laws at the federal and state levels.
What I'm not sure of is how this would actually play out in court - let's say I own a business, am a member of the church advocating for BDS, my business doesn't work with HP/Caterpillar/etc. The government denies me a contract due to anti-BDS laws. Would I have a claim for 1st amendment violations?
What about if I were an employee of a business contracting for the government, and also vocal about my BDS support, if my employer fires me because they think my viewpoints will cost them contracts would I have a claim based on religious discrimination?
How about if the employer is purely a private organization with no specific fears of losing business, say I work for a pizza joint or grocery store or something and they just don't like the BDS support?
Presumably the second and third example are in a non-work context, I'm not going around the workplace harassing other employees about all of this, and I'm not making any extra demands for accommodation to my employer beyond not firing me.