Salem is, AFAIK, a privately held, for-profit company.
Just to set the record straight, Salem Communications is a "publicly held" for-profit corporation. Any member of the public can buy shares in Salem on any day the stock market is opened. Salem Shares trade on NASDAQ under the symbol: SALM
As a "public company" Salem's records must be open to the public.
You will find a lot of financial information on Salem here:
http://www.reuters.com/finance/stocks/companyProfile?rpc=66&symbol=SALM.O
I think what you meant was that unlike other religious broadcasters, Salem is for-profit. Other religious broadcasters like Family Radio, and Pillar of Fire are non-profit and tax exempt. But they also must make all their financial records available to the public since donations to them are tax deductible.
Either way, these organizations cannot discriminate against anybody solely based on their religious beliefs, but they can hire anybody they want and have other standards that they go by. You can be sure they don't have a written policy that says "only the very monotheistic religious may apply." But, they could prefer to hire graduates of the "Moody Bible Institute" instead of Harvard or MIT because they think Evangelically educated people would be a better fit in their organization.
By the way, about 40-percent of Salem's shares are held by institutions, like investment funds, pension funds etc. You can be pretty sure they do their homework on how Salem is run, and Salem most likely plays by the rules because of all the scrutiny.
And besides orthodox Jews as prominent program hosts, they have Bill Bennett who is Roman Catholic.
The bottom line is:
If the law says that such companies cannot refuse to hire individuals whose political views are at variance with those of the company's owners, my impression is that media companies must have an exemption.
Media companies are NOT exempt, and because of their high visibility and broadcast license holdings are under even more scrutiny than most companies and have all sorts of publicly available records to prove they don't discriminate based on political or religious beliefs or affiliations. They probably don't even ask about those topics during the hiring process, that is Human Resources 101 stuff that is strict policy at most larger corporations in this country.