I will discuss how we definitely know that objective morality is true and subjective morality is false. I will cover 4 contingent grounds that back up the morality.
Objective Morality is true
The reason objective morality is true is partly due to any observation of good or evil must yield from a grounding source. Over 96% of people believe this source to be God but despite whether God is the source or not, it is easy to show the source has objective roots. Anything you name to be good is good whether or not you say it is good. Let us say that you get the revelation that choosing to extend your life without as much stress and pain is good. Well this will be good for all and not just good and would be good even it you said it was evil. Let us take evil for example. Any evil action is evil even if you say it is good. If you burn people at the stake for walking on your property by tying them up, then doing it, it is evil and the evil is always evil even if you say it is good. Your observation of the action is not opinion but is a set standard of evil. No matter who does this act, it is evil and the reason doesn't matter. If they are mentally healthy, they will be held accountable for their evil deed.
Subjective Morality is false
Subjective morality is easy to show false. Anything that is left to opinion would not get an outrage from known people showing their emotions. Let's say that a person says that maximizing well being of a person is moral. Then their standard is of objective value even if they claim to be subjectively applying principles to it. There would be a set way to determine what moral action was done. Also, lets say a person says it is my opinion that rape is evil and that their opinion is that rape is good. Well using their claimed standard of maximizing well being as being moral, they contradicted their stance. If an action was truly subjective, then no rage would one. People rage when hearing murder being a chosen action of an evil person or end up very thrilled to know a person saved their cat from a fire. If these actions were subjective as being moral, then their expressions would be not be indicative of a known evil versus a known good action. Liking anchovies on a pizza is an opinion. Choosing whether murder is good or evil is not an opinion but objectively good and our expressions match so.
Confusing ideas of objectivity and subjectivity
The main reason people think thinks are subjective that have an objective root is due to their sinful nature wanting to be in final control of their life and everything and not depending on the eternal source of morality to make our choices. It is human nature to want to be in control. People think that whether or not rape is moral or immoral is akin to whether or not anchovies on a pizza is lovely tasting or gross tasting.
Good versus evil are opinions without God
If you are a denier of God's existence, then there is no good and no evil in your view even though you are unaware of that. Anything would go. To rage at what you call evil, would be futile if there is no Hell to go to for it. If you ended up feeding the hungry and I murdered 3 people and we both died in a car wreck in a few hours and our deeds went unpunished, then it is asinine to call what you did good and what I did evil since there must yield an objective standard to differentiate the good from the evil but morality must transcend our title of saying it is good or evil and yield a result. If we both had an afterlife of nothingness, then your good and my evil would be equal. If we just made up terms to be good or evil, then you are objectively thinking your standard is the standard by which you should get mad at if people violated. If a person ended up doing something you think is evil, you would rightly rage because you know evil must be punished. If you think it was subjective, you wouldn't rage when others aren't living up to your standards of morality.
People want to dictate what is objectivity and what is subjective in terms of morality. People like being in control and not depending on the source if morality. Nobody can be their own source of morality. Any observation of morality is misinterpreting it. Morality is objective and there is nothing you can do to change the fact that if there is no Hell, there is no evil. Evil must be punished and you know it. Good must be rewarded. Whether you do it for those reasons is meaningless because if left to opinion for everything, anything goes and that is chaos. Thanks for reading!