A boycott of any US company (or US entity doing any kind of commerce) in which one involves others, or is a non-active agent ("supporter"), is illegal in the US by federal law. Period, no question of there being any connection to religious reasons.
Admittedly, it is winked at and certain people have made fortunes organizing boycotts and threatening to do so. (Rev. Jesse Jackson made as much as $70,000,000 one year in donations after "exploring" the organization of such boycotts against the donating companies whom he then... felt were not deserving of boycotting.) But it is still against explicit federal trade law. And certainly, no US Attorney ever brought a case against those boycotting US companies that did business with South Africa so... "winked at" seems to be the rule to a jaded soul like mine.
Boycotting Israel is illegal by federal law in any contract that crosses US borders. That means any importing or exporting along with anything else that fits. I said it that way because an exporter, for example, like my company is breaking federal law if it even accepts a contract that has hidden away in boilerplate the requirement to not do business with Israel. (So we don't do business with Muslim countries. Period. Do not seek their business, do not respond to the VERY occasional inquiry. Because they are often REQUIRED by their own laws to insert such clauses into every contract. They have to do it by law and we cannot just nod and ignore it, by law. So we have no basis for business. Obviously, not all do of course, and some lie, of course, about the "it's our law, sorry" but we don't care to be ground between either government or polity.)
In neither of the cases above is there any religious underpinning, except perhaps in some very indirect way. It's simply one government demanding its citizens do not undermine its foreign policies goals and obligations for a pile of cash.
So one or the other kind of situation would almost certainly cover any "anti-BDS" law you are aware of. Invalidating it. No religious aspect involved in the invalidation.
So it is hard to see why a Constitutional aspect need arise. Though it is definitely an interesting idea. The problem with it though is that the Constitution doesn't have any problem with support of religion in general, just in "establishing" a particular one. And I don't see how having or not having "anti-BDS" laws would "establish" any particular religion.