Political opinion is protected (Article 3 GG), provided the opinion does not violate the rights of others. This leads to a complex system of rights and exceptions.
For instance, a newspaper is a so-called Tendenzbetrieb, it is allowed to discriminate among their editorial staff based on the political opinion of the paper. If they have a subsidiary handling the printing, that would not be a Tendenzbetrieb and could not discriminate. And not all political opinions are equal. One which has been found to promote the overthrow of the constitutional order is not protected.
As pointed out in the answer by ProgrammingMachine5000, the Grundgesetz article does not directly bind non-public actors. However, it requires the legislative to enact legislation protecting it, e.g. Art. 75 BetrVG, which again mentions political views as a protected characteristic, but also Recht und Billigkeit (equitability). While ProgrammingMachine5000 quotes the example of a hotel owner being allowed to refuse guests, I quote the example of an employer not being allowed to fire employees ...
One might also note that the case mentioned by ProgrammingMachine5000 involved a leading NPD figure, a party which was labeled by the supreme court as holding anti-constitutional views.