The second is that you judge some aspects of the Bible immoral, but you have no standard on which to base those objections if there is no higher authority. If morality only comes from social agreement then why would someone from one society have any moral basis on which to judge someone from another society? This is the exact thing you attempt to do when you claim that burning a fornicator is immoral.
I think you're missing an important distinction and setting up a false dichotomy. The false dichotomy is that one does need to believe in a god to believe in objective morality. There are objectivist systems of morality that don't involve a deity. Furthermore, it's possible to hold a moral standard for oneself without considering it objective.
The distinction is that relativism need not be the belief that anything goes. It can be the belief that one society's morals are as good as another, but more often, I think, it's an observation of how morality works in practice - that is, generally speaking, morality is socially received. There's meta-ethical relativism and there's ethical relativism.
The former says nothing of the quality of socially received morals, nor does it say that exceptions to the rule that morality is socially received are impossible. It would be absurd if it did: it would take only one person with morals contrasting with those of their society for this to be false.
When exmaning society's morals, you're examining aspects of a culture, not aspects of the behaviour of individuals. It will be unlikely that anyone fully adheres to their society's morality. It will be equally unlikely that their culture contains a moral system which weighs in on every aspect of their life, so there will always be room for individual morality even within a relativist conception of morality. If your society's one rule is "Don't pee in the water supply", the way you conduct yourself in every other aspect of your life will be decided by something else. Of course, your society (or another group - this need not be cultural relativism) could have very strict, traditionalist rules about almost everything, but there are always rebels, and even then, they're unlikely to have a inviolable protocol regarding everything.
So with regards to personal morality and relativism, several things are possible:
1. Your 'anything goes' scenario, where a person considers all actions to be morally neutral because morals are just social rules anyway.
2. Relative moralism, where a person considers all actions that contravene the moral standards of the society in which they occur to be immortal.
3. The observation of relativism in conjunction with a non-relativist moral system, where a person believes that morals are socially constructed, but that objective morals can be constructed by other means, and attempts to do so.
4. The observation of relativism in conjunction with a separate relativist moral system, where a person believes that morals are socially constructed, but has their own morals constructed by another system which they do not consider to be objective.
These may exist among others; they're just the ones that spring to mind. In any case, I fall under number 4. I have a moral standard for myself.
I'm not interested in telling others how they should behave - for one thing, I don't believe they had a choice - but I consider it my duty to encourage 'good' actions. Deterministic as the universe may be, in any case my own actions will play a part in determining what occurs, including exhortations for others to do good, and my awareness of that will play a part in determining my own actions.
I also consider it my duty to do everything in my power to prevent morally wrong actions - for instance, intervening to stop a rape or murder. I am not interested, however, in insisting that others do the same - encouraging them, perhaps, but I don't believe in nonconsensual impositions of my beliefs on those who may not share them. When they attempt to do the same to others, I consider it right to intervene - this is not an imposition on them, as they remain free to
try. It's merely ensuring that their attempt fails. They retain the freedom to express their will through actions, but the right to the realisation of those actions is not a given. It's the equivalent of following around a missionary and offering an alternative to their preaching.
Honestly, I consider the Christian standard too low for myself, so I object to the idea that it's impossible to have a moral standard without having a god. The moral standard you base on your belief in a god seems lacking to me, I would endeavour to be better than that.
@jameslikespie re: Dawkins: I think he has a rubbish definition of religion and I disagree with his views on group selection theory. Challengers are starting to emerge (gene-culture coevolution, or "cultural evolution", is the one I'm thinking of primarily, but multilevel selection as well) that seem far more capable of accounting for altruistic behaviour towards genetic strangers. I really like that George R Price, who was instrumental in developing group selection theory, ended up being deliberately as selflessly altruistic as possible to complete strangers in an effort to prove himself wrong. Before he cut open his neck with a pair of nail scissors in a final act of defiance against his genes, that is.