The mental gymnastics on this thread are insane. I can't believe that adult, presumably moderately to highly educated people are jumping through insane mental gymnastics and reading laws and regulations for the very first time and trying to jump to conclusions and defend an unsupportable position.
There are numerous carveouts in the ACAA that gives some latitude to carriers of how to validate fitness to fly. Regardless of whether or not you think this is a stretch, the reality is that there is more than enough reasonable grounds for Delta to conduct this screening measure that there will be no quick regulatory backlash - at worst it would gum its way though courts. My initial readings of the relevant ACAA materials it seems pretty clear that this is allowable, but quite frankly my interpretation is irrelevant as I do not specialize in aviation law and and regulations. Even for those on this forum that may have formal legal training and/or be practicing attorneys, unless your full time job is in aviation law or have spent at least the last three months studying the case law and full regulatory guidance around all relevant acts, your opinion is basically worthless because of the specialized nature of these regulations.
As a general statement, anyone who takes issue with wearing a mask on a flight has no right to fly. If you read my post history, you will see I am one of the most civil liberties-focused posters on this forum with regards to security theater, privacy, free speech, or a myriad of other topics. I don't care whether you do drugs, I quietly rage every time I am forced to present ID to the TSA or have my electronic devices seized consistently by the CBP despite being a US citizen, and will fight to stop the criminalization of hate speech - regardless of how disgusting and insensitive that language may be. But your rights do not extend to the right to harm others. The best understood scientific consensus related to COVID-19 and related families of viruses indicates that masks help protect others - and not at "statistical noise" levels but significant reduction in transmissibility. Whether or not you want to expose yourself is your choice, but it is not someone else's choice to have you expose them.
There are huge rights violations that happen every day. There is plenty of room to protest against authoritarianism or the massive erosion of individual rights in an increasingly Orwellian panopticon security state. Fight those battles. Complaining about wearing a mask to protect others is the most immature, nonsensical, and self-defeating position you can take - especially when mandated by a private entity like an airline that should have more - not less - latitude on who they allow to fly them than they do today.
Delta is in the right to strengthen its mask regulations. There are virtually no legitimate medical carveouts to not wear a mask while still being fit to fly. The only one I can moderately think of are highly autistic children (or highly disabled autistic adults) with extreme hypersensitivity to unusual touches. Other than that? If you can't wear a mask, you're almost certainly not fit to fly.