Not exactly. Johnson was more a Democrat than anything else, though admittedly he was not elected President.
But Grover Cleveland was, twice. Non-sequentially, the only President to achieve that feat.
Yes, you are right. I didn’t include Johnson because he wasn’t elected, but you’re right on Cleveland. However, Cleveland was more conservative and “more Republican” than most Republicans of the Day. It would have been akin to electing an Ed Koch or a Charlie Wilson.