Political campaigning church lost 501C3, would Anti-discrimination laws apply now?

Let’s say a church or non-profit, like the Waynesville Church, violated its 501©(3) tax status by campaigning for a candidate per the IRS:

Should that happen, do they lose their ability to discriminate on membership, employment, etc?

For example, the Boy Scouts of America start campaigning for candidate X. They then lose their 501©(3) status. Would the BSA also lose the ability to not hire atheists based on anti-discrimination laws?