The position that some of God's laws are not moral laws is the position that we can be acting morally while disobeying those laws, however, there are no examples in the Bible where disobedience to any of God's laws is said to be moral and I do not see justification for thinking that it can ever be moral to disobey God. Morality is in regard to what we ought to do and we ought to obey God, so all of God's laws are inherently moral laws. Legislators give laws according to what they think ought to be done, so the position that some of God's laws are not moral laws is the position that God made a moral error about what ought to be done when He gave those laws, which is claiming to have greater moral knowledge than God.
All of God's laws are either in regard to the way to love God or the way to love our neighbor, which is why Jesus said in Matthew 22:36-40 that those are the greatest two commandments and that all of the other commandments hang on them. So the position that we should obey the greatest two commandments is also the position that we should obey all of the other commandments that hang on them, for example, if we love God and our neighbor, then we won't commit adultery, idolatry, theft, murder, kidnapping, favoritism, rape, and so forth for the rest of the Mosaic Law.
In Romans 7:14, it says that God's law is spiritual, not that some of God's laws are spiritual while others are not. In Psalms 119:160, all of God's righteous laws are eternal, so none of them will ever pass away.
In Romans 6:14, it describes the law that we aren't under as being a law where sin had dominion over us, which does not describe the Law of God, but rather it is the law of sin where sin had dominion over us. In Romans 6:15, being under grace does not mean that we are permitted to sin, and in Romans 3:20, it is by the Mosaic Law that we have knowledge of what sin is, so we are still under the Mosaic Law, but are not under the law of sin.
In Galatians 5:16-18, Paul spoke about the desires of the flesh as causing us not to do the good that we want to do, which again how he described his struggle with the law of sin in Romans 7. The Spirit is God, so it wouldn't make sense to think interpret that as saying that we aren't under the Law of God when we are led by the Spirit, especially when the Spirit has the role of leading us to obey the Law of God (Ezekiel 36:26-27).
In Colossians 2:14, it says nothing to distinguish between physical or spiritual ordinances.
1.) You shall not commit murder.
2.) This person has been found guilty of murder.
The first is an example of a law that is for our own good while the second is an example of a handwritten ordinance that was against someone that was nailed to their cross in order to announce why they were being executed. This fits perfectly with the list of sins that we have committed being nailed to Christ's cross and with him dying in our place to pay the penalty for our sins, but has nothing to do with nailing any laws to the cross. In Titus 2:14, it doesn't say that Jesus gave himself to free us from any laws, but in order to free us from all lawlessness.
Correctly understanding a spiritual principle will lead us to take physical actions that are examples of that principle in accordance with what God's law instructs. If someone thought that they understood the spiritual principle of love, so they did not need to take physical actions to express love for their neighbor, then they would be missing the whole point.