Should taking public money compel you to comply with federal and state law?

It came as little shock to most folks here in the US of A when we were recently declared an oligarchy rather than a democracy. Also not really a new observation.

In past times, when the influence of the oligarchs became too onerous we passed laws to protect our citizens from the worst of the abuses. We passed labor laws, civil rights laws, laws requiring accessibility and accommodation for the disabled. These laws were enacted both by states and on a federal level.
As with most laws, negotiation and compromise resulted in some exemptions to those laws.
In general, 501c organizations are exempt from many of these laws - this wikipedia article has some good references on this: 501(c) . Although 501(c) is the definition of federal tax exempt organizations, but it has been used as the basis for determining exemption from other requirements as well.

NFL Headquarters

So now we are seeing these exemptions being used by large employers out there, who are receiving a lot of their money from state and federal coffers.
501(c) organizations are also now allowed to pay substantial salaries to their "insiders" as well as conducting lobbying. Rather than these sorts of exemptions and tax breaks being only applied to your local synagogue or boys club, these are also being applied to large church-affiliated medical systems, the NFL , insurance companies , and more.

What this means is that while these companies can be recipients of federal and state funds, grants, get preferences on federal contracts, etc. they are exempt from labor laws that apply to everyone else. This does not mean that they CANNOT abide by these laws, but that they MAY not abide by these laws. My experience in the workforce has been that companies comply only to the point of MUST, not to CAN.
So what does all this come down to for you and I?

 

 It means that if you choose to work for a non-profit, for a tribal entity, for a faith-based institution then you can expect that you will have no job protection should you become ill and require accommodations. It means that all those folks who are taking care of you, who are serving you, who are watching your kids in those organizations also lack that protection.

It also means that groups like Hobby Lobby and faith-based hospitals are going to try and claim exemption from other federal requirements like compliance with the ADA.

Shouldn't organizations that are exempt from paying federal taxes, that are receiving federal and state money such as medicaid and medicare, grants, and getting other federal benefits at minimum be required to comply with federal and state labor laws?