The correct option is
B say they agree that Americans are capable of self-control while acting otherwise
The phrase 'pay lip-loyalty' means 'to express loyalty or support for something insincerely'. Thus, Roosevelt is saying that 'while the opponents say that they agree with the idea of American people having self-control, their actions indicate otherwise'. Thus, the answer must have the above meaning.
Option A is incorrect. It means the opponents truly believe that American people are capable of self-control. Thus, it does not have the required meaning.
Option B is correct. It has the exact required meaning and thus, it is the correct answer.
Option C is incorrect. It means that the opponents support people's right to rule, but not during war time. Thus, it has no connection to the required meaning.
Option D is incorrect. It says that the opponents give many speeches saying that they agree about American people having self-control. Thus, it does not have the required meaning either.