The reason morality isn’t objective is because those touting objective morality usually make blanket statements such as “killing is bad”.
But morality, like the law, should be taken completely objectively.
Now, I’m an atheist, so obviously I know that morality doesn’t come from a single book, but nevertheless I know that morality is objective.
Morality is objective, because once the context is clearly and specifically defined then the resultant morality is certain, it is not subjective.
You can’t base a definitive answer to morality on a broad context, but you can have a definitive answer for a very specific context.
And that is what the law should be if it isn’t already- just a lot of specific crimes and contexts and judgement for each and every one of them.
Therefore, morality is objective.