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.

This started as a discussion about whether not-primarily-political institutions (like Scientific American) should have and publish political opinions. It was started by an attack of a political institution (Reason) saying they should not. That attack itself makes the target politically relevant.

Bakeries are in a similar position. Once an owner declines to serve a customer based on his (owner or customer) political leaning, it's politically relevant. If a politican attack bakers because (he feels that) the bread price is too high, it's politically relevant. I think there was an American civil rights movement in the 60's which was in a great part about equal access to services for all ethnicities. Was that not political?

> they are not concerned with the organization of government and policies

'or public affairs'. You wanted a definition and then you are ignoring it?