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You also don't have to give your money to the airlines
Air travel is not a right protected by the constitution. You don't have to submit to "groping," nor to a dose of radiation that is lower than that of a transcontinental flight itself. No one is stopping you from going anywhere you wish to go. Trains, buses, cars and your feet are perfectly acceptable alternatives.
Your modesty does not outweight the safety of the other people on the plane.
And let's be realistic about your 4th Amendment rights. The key word in that phrase is "unreasonable." Again, you don't have to fly, and therefore, you don't have to submit to anything you don't wish. Therefore, your rights haven't been violated. If you want to use this wonderful form of travel, in which you are in a plane with hundreds of other people who may have differing views than you, then there are proceedures you have to follow. That's the free market.
If enough people stop using air travel, the free market will dictate a change. Participate in the opt-out protest. If people do not stop flying, it will be because the majority have no problem submitting to safety checks, and this process will continue.