Let me add further.
When you sit on an airplane, in flight, you are in a transport vehicle owned by a private corporation, yet regulated by the State.
Think you have any property rights there?
The rights referred to in the Constitution do not exist in transactions between businesses and individuals, except insofar as Congress has provided through regulation of interstate commerce (the Civil Rights Act of 1964, for example).
Hence, while you are riding in someone else's airplane, you cannot make a speech, carry a gun, quarter a soldier under your seat. You are not free from unreasonable searches or seizures, as long as they are not carried out by an agent of the government. You may not freely exercise your religion. You may not peaceably assemble in the aisles or toilets. And so on.