What specific provision do you think would enable lawsuits against those you mentioned?
Look up the Supreme Court decision that allowed IRS to strip Oral Robert’s U of its tax exempt status because it prohibited interracial dating. The decision relied on the fact Congress had passed national laws against racial discrimination.
So now, with a congressional law affirming same sex marriage, the ground is set for lawsuits against the tax exemptions for churches, schools , adoption orgs, etc if they don’t also affirm same Sec marriage.