Its true that all morals are subjective but that does not make them wrong. It can make them wrong to certain individuals but it doesn't create a wrong in all cases.
In actuality everything is made up, unless you believe in higher power(s), and people tend to morally align themselves with whatever group they are associated with.
Then saying its right or wrong is wrong. This is like saying the eight ball is a solid or a stripe when its neutral. Im getting so sick of hearing people who claim morality is subject talk about proper morals. Im also getting sick of christians talking about proper punishments for crimes when they believe in a god who punishes people eternally not for their crimes but for not believing while he sent an innocent being to be punished for our sins. These people have no clue what true justice is and im tired of hearing them speculate. There are a lot of things im getting sick of on this site. Either start making sense or stop talking.
In short relativism is also relative.
Morality is just opinions about what ought to be. But in recognizing this that doesn't give me a duty to be indifferent about everything. I care about things so I will try to do what I can for those things and to persuade others to care too. I care about being alive and about the people around me being alive, so accordingly I judge people who commit murder and believe they should go to prison. Is murder being wrong subjective? Yes, but that doesn't mean I have to tolerate it, since whether or not to tolerate something is also subjective. Fortunately I live in a society where the vast majority agree and where we are capable of organizing things like police and courts and prisons in order to enforce against murder and other things I find immoral.
Recognizing it is all subjective though I am able to think logically about whether something done privately affects me. Murder, rape, theft even if done in private affect me because I or someone I care about could be a victim. Fetishistic sex acts that I may personally find disgusting on the other hand when done in private and between consenting adults don't affect me. And some of those same people may contribute greatly to society and hence to me and those I care about. So I personally find something disgusting but at the same time recognize that nobody benefits from laying the long arm of the law down against people who participate in the act. Plus I may enjoy things others find disgusting. A social contract whereby if it doesn't affect other people it is allowed in private is mutually beneficial in terms of liberty.
Your premise asserts that morals are subjective and therefore have no basis in terms of an absolute right or wrong. The very idea of moral relativity asserts that there are no rights or wrongs. Therefore, the conclusion at which you have arrived negates this first assumption, and is therefore incorrect.
You do realize that "wrong" is also subjective, right? Morals are useful guidelines when pursuing a goal, but are dependent on that goal. To say that something is morally "right" or "wrong" is simply to say whether it is more likely to benefit or detriment that goal. Because the exact outcome is never certain, however, such guidelines are only guidelines and do not apply to every situation. They must be supplemented by an individual's logic and judgment.
Ethical statements are not facts, they are matters of opinion. A philosopher named Alfred Ayer argued that statements only have meaning if they are analytic or empirically verifiable. The "principle of verification" therefore implies that ethical statements are meaningless in a cognitive sense. They are more expressions of emotional attitude.
Morals end up being shared. Where they are common, or consensus is seen, you read in "objectivity". Objectivity that does not exist, only is a condition of commonality.
I don't know why anyone gets overwrought about this concept. I can see objecting to an individual moral stance, but not the concept.