This is not true. You don't have to renounce your humanity to follow Christ. This could only be said by someone who has not experienced His love and forgiveness.
As far as liberty goes, you will always be subject to a power in the unseen realm. Choosing God over his adversary brings us into alignment with the intended order of this now corrupted world.
Liberty is different from licentiousness and often confused with it. Being set free from the bondage of sin would be liberty in this case.