Am I allowed to transfer it to another maintainer or could I be somehow liable for transferring their IP?
The important thing to remember here is that "ownership" of a repository is purely an administrative thing; transferring a repository does not of itself mean any transfer of IP occurs. You will continue to own the rights to any code you wrote and any other contributors will continue to own the rights to any code they wrote. The new maintainer will be exercising their rights under the MIT license "to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so"
Can they ask for their contributions to be removed if they don’t like the new owner?
No; it is generally accepted that a grant of rights under an open source license is irrevocable.
Basically, what are their rights in this case?
Not much. Once you license your content under an open source license, you are largely giving up all control of it in the future other than the restrictions in the license itself.
And what happens if the new owner turns out to be adversarial and removes the MIT license?
Then they would be committing a copyright violation, as the only right they have to use the software is under the MIT license, which requires that the license is distributed with the software.