I just think we are talking about different things. I hear what you are saying, but I don't think that bakeries being tangentially related to politically charged topics make them a political institution.
Bakeries also handle and store money, but that doesn't make them a bank. etc. The nature of bakeries as an institution is not political - they are not concerned with the organization of government and policies. They may interact with the government but that doesn't make it a political institution.