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

[stpauler]

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:

@IRS

it may not attempt to influence legislation as a substantial part of its activities and it may not participate at all in campaign activity for or against political candidates.

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?