Well, the Constitution does say that treaties are legally binding, so you’re painting a false dichotomy between treaties and the Constitution. That’s why we need to actually withdraw from these treaties. I agree with the libs on one thing on this issue: the rule of law matters. So we need to change the law and keep pretending we care whether a few terrorists get dunked in the water.
In fact, if you read the inter-American weapons treaty that Obama wants the Senate to ratify, it spells out explicitly that it is limited by the Constitution of ratifying states. Moreover the US Constitution prohibits international treaty from abrogating US Constitutional law. The Senate can abrogate or vacate an international treaty with the same 2/3rds vote that is required to ratify.