As a general rule, your right to free speech ends when you set foot on your employer's property. You can be fired for anything you say while representing your company.
HOWEVER, an organization that receives taxpayer funding should be more open. Religious based programs have lost funding because they refused to hire gays, transgenders, or just non-members of their denomination.
Churches can lose their tax-exempt status for getting too involved in politics.
If National Public Radio wants to continue receiving public funds, then they should allow all opinions, offensive or not. If they want to filter broadcasts according to one political vision, they should give up public funding and compete for advertising dollars just like every other news organization.