Biblical Covenants in Christianity
Christians routinely speak of the OC† and the NC (old and new covenants, respectively) when equivocating from the harshness of the Mosaic laws in the Old Testament such as Leviticus 20:13 which calls for the death penalty for homosexual acts or the various rules on how to properly enslave another human being, etc. In particular, moral, ritual and ceremonial laws such as those found in Leviticus and Deuteronomy which are directly attributed to God ("The LORD said ...") are deemed to be obsolete by some Christians due to Jesus' death and the NC which was brought forth. Other Christians believe that only some of the OC is replaced and the rest intact. (Note those who deem homosexuality an abomination in the eyes of God.) Others even claim the entire OC is part of the NC.
The problem, of course, is that unlike the OC where one can list 613 laws, there is nothing definitive about the NC. This ambiguity (and, indeed, absence of definition) allows Christians to make any vague claim they wish about the NC.
In short, the claim 'that was the OC, we are now operating under the NC' is meaningless because nobody has a specific definition of the NC. The New Covenant is a concept devoid of defined content. It is a contract with an opening paragraph but no details. Christians fill in the blanks however they wish and thus the specific meaning for the New Covenant is all over the map.
† the OC in Judaism has a very different meaning than how Christians use the term.