It depends. The rationale for the taxicab exception is the same for ride-sourcing companies when a public transit agency has a contractual or other arrangement with two or more ride-sourcing companies or taxicab companies to provide a specific service or type of service, and the public transit passenger chooses among the providers. In this case, the public transit agency would have to contract with at least two ride-sourcing companies and/or taxicab companies to ensure the passenger has a choice of which provider to contact for a ride.
There may be some situations in which a public transit agency contracts with two or more ride-sourcing companies as well as one or more taxicab companies in order to ensure the service is available for all passengers. For example, the taxicab company may be the only contractor with accessible vehicles, or may be the only contractor able to schedule trips over the phone or accept cash payment from passengers. While some passengers may have only one choice, this does not change the fact that many passengers will have more than one choice, and so the taxicab exception will apply to all of the providers.