Your questions are perfectly in order. If position A and position B are logically contradictory, they cannot both be true. (They may, of course, both be false!)
However, if you don’t mind, I’m going to take a little pause before attempting to answer them because any kind of even semi-adequate answer will take me some time to put together and I’m working flat out at the moment to finish the first part of the lecture series on political philosophy that I promised Dr Woods. With a bit of luck, I should be able to get back to you towards the end of next week.