The gamerule ‘commandblockoutput’ has no effect on the output of command block minecarts. The command block minecart’s output is dependent on the gamerule ‘sendcommandfeedback’, which is incorrect behavior.
Expected behavior: minecart with command block will not output commands when the gamerule 'commandblockoutput' is set to false
Exhibited behavior: minecart with command block continues to output commands, regardless of the value of the gamerule ‘commandblockoutput.’
It does have an effect, just not on the /tp command. This is the same for the regular command block. This behavior is intentional per MCPE-65746.