On another thread about this, a poster wrote that Rand Paul typically "dresses down" when traveling, so that he isn't as recognizable. I'm curious if he even identified himself as a US Senator, and if anyone at the TSA checkpoint was knowledgeable enough to recognize him or even his name.
Even the TSA is smart enough to realize the political fallout from harassing a US Senator. They got a huge black eye back in 2004 because Ted Kennedy was stopped repeatedly because he had a name similar to "T. Kennedy" on the secret "no-fly" list. I believe it eventually led to the "redress number" system where you can get certification that you aren't the person on the no-fly list, even though you have the same name.
BTW, there is a similar law in Texas. Every legislative session, the Texas Dept. of Public Safety issued a "blue card" to every Texas legislator. It identified them as someone that the DPS should not detain. I don't know if other law enforcement agencies honored it.
However, I don't think the DPS issues it any longer. There were some abuses of the card years ago, and I think a legislator that was DWI went on to be involved in a serious accident after the DPS didn't detain him. But, I may be misremembering it....
Original intent both federal and state is to prevent opposition from detaining by law enforcement as a means to change the outcome in a House or Senate vote.
If they are detained and not present they cannot vote.