Nope, it's a common carrier, and they are prohibited from discrimination based on any class.
https://www.law.cornell.edu/uscode/text/47/202
It shall be unlawful for any common carrier to make any unjust or unreasonable discrimination in charges, practices, classifications, regulations, facilities, or services for or in connection with like communication service, directly or indirectly, by any means or device, or to make or give any undue or unreasonable preference or advantage to any particular person, class of persons, or locality, or to subject any particular person, class of persons, or locality to any undue or unreasonable prejudice or disadvantage.
Chapter 5 applies to wireless or radio communication, not airlines.
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