I've explained this exact thing to cis people multiple times. I often just brace myself before every flight to get a pat down. They always look shocked and horrified by the information.
And the funnest part of it all is airport security fucking sucks at their fucking job. The TSA in particular are so shit at their jobs its almost insulting. I get a pat down every time I show up, but my friend accidentally made it ALL the way through the airport and onto a plane with a loaded hand gun in a holster because they forgot they had it on them! And the TSA didn't catch it or do fucking shit about it!
this video only covers how trans women are affected, probably since that's what she knows and can speak to, but everything she mentions applies to transgender men and nonbinary people too, often in the exact same way
if you register as male and they hit the blue button, but your chest registers as "suspicious lumps," you will get a pat down
if you don't register as male and they hit the pink button, your dick or packer will get flagged and you will get a pat down
if you still have both a chest and a dick / packer, you WILL get a pat down
regardless of this, if your ID doesn't match what they assume you are or how you present, you will get a pat down and grilled on why you have a fake ID / are trying to impersonate someone / lying to them
if you managed to get your ID (driver's license) changed to your gender through a court order but can't get your birth certificate changed (due to state laws specifically prohibiting it), you might have a lot of trouble getting your passport updated to your gender. or you just haven't had the time or money or spoons to get both changed! getting my ID changed to male cost me $500, a month of stress, and a day of getting misgendered in court while having to publicly beg a judge to acknowledge me
there's a lot of things can get you clocked, flagged, and endangered, and this can apply even to cisgender bodies too. not adding this part as a "think about the poor cis!" but "this is how much the machine and the system is fucked"
people with prosthetics can also get flagged, assistive devices can get flagged, fat people who exist while being fat can get flagged ("suspicious lumps"), cis women who aren't performing femininity can get flagged, cis women who just aren't white can get flagged,
the list goes on