Southwest Airlines plane. DALLAS - Southwest Airlines says it will go against Texas Gov. Greg Abbott’s latest executive order and instead comply with President Joe Biden’s mandate requiring employees to be vaccinated.The Dallas-based airline carrier made the announcement Tuesday morning in response the order Abbott issued Monday."No entity in Texas can compel receipt of a COVID-19 vaccine by any individual, including an employee or a consumer, who objects to such vaccination for any reason of personal conscience, based on a religious belief, or for medical reasons, including prior recovery from COVID-19," Abbott wrote in his order.RELATED: Gov.