Firstly I will distinguish between moral choices and moral standards. Moral choices are always a matter of subjectivity. Everyone decides which moral standard to follow and how rigidly to follow it. Most often we base our moral standard on how we would ideally make moral decisions. This is not a matter of debate. I am not arguing which moral standard is the most persuasive or beneficial to have, as that depends on what you wish your moral standard to be beneficial TOWARDS - a matter of subjectivity.
What I am asserting is exactly as the title of this thread implies - that no matter your religious belief, you are capable of having an objective moral standard to make moral choices by.
The majority of Theists have long claimed monopoly on their basis for morality, but why would this be? Because they have their standard in literal, non-negotiable wording? If that were the case, they would acknowledge any moral standard presented in writing by non-Theists. Instead they choose to call morals of non-Theists subjective or based on their own personal feelings/reasoning. What this entails is that the Theistic basis for morality is not a choice at all, and that they are obligated to live by this moral standard whether they believe it is morally right by their own internal feeling-based standard or not. I will not argue that belief in a certain religion is a choice, as belief is rarely ever a choice unless under certain extenuating circumstances. Pascal's wager is not a valid idea because Atheists cannot choose to be Theist at whim. They must be thoroughly convinced of the logical consistency of it.
So is following the moral standard internal to your Theistic belief a choice? Yes. Whether you raise the point that this moral standard is phrased as a commandment or not, you ultimately have free will in following this standard. I can command that you believe in everything I say, but you still probably won't believe it unless I persuade you. This also applies to God. A command is to be taken on your own personal merit. If your merit is absolute servility to the being giving you command, then you still choose to follow the command because of your merits. It wouldn't be a command if you had free will in following it. It would be forced obedience. You would have no say in the matter whatsoever were it not a matter of choice. Some circumstances objectors may mention are standards which compel you to follow them so intensely that you delude yourself into having no choice. An example of this is someone believing wholeheartedly in the Bible and desperately not wanting to go to hell but not being wholly convinced by wanting to be obedient to Yahweh. Well then, this isn't a choice at all, and it isn't based on logic or reasoning but rather on your desperate desire to follow one course of action over another. What does this mean? It means that some people are insane. Some people aren't able to live or make decisions by a logical standard, so logically refuting them will not work. There is no possible objection I can make to someone who believes so intensely in the Bible that they will sub-consciously give themselves no choice whatsoever in the matter. I am not making this argument for people who brainwash themselves. I am making this argument for sane individuals.
Now since I have hopefully shown that following a moral standard is a choice, I have determined that it is a decision you will make based on your own personal reasoning/feelings and therefore subjective... sound familiar? If your choice of moral standard is subjective, then ultimately Theists are calling their own choice to follow the commandments of the Bible a subjective choice based on their own desires and reasoning. What this means is that your choice of a moral standard is absolutely dependent on yourself. If your objective in life is to cause the highest degree of suffering to others, then you will likely choose a moral standard which reflects this. I haven't met anyone who wholeheartedly wants everyone and everything to suffer, but I'm sure that it is a possibility Theists are willing to point out because they think it refutes my argument. No such luck. Choice of a moral standard aren't something to establish objectively because they rely on preconceived ideals and goals. This is no longer a topic of debate unless you are convinced that your technique of self-brainwashing gives you absolute certainty of your choice in moral standards and that you are immune to logic. I say that this is no longer a topic of debate with about 99% certainty. I may be completely wrong and simply be awaiting some proud moral objectivist crusader to come along and show that all of my logic is riddled with logical inconsistencies, but I doubt this very much.
Now on to how moral standards specifically can be objective given a certain criteria to work by. If your primary goal in life with morals is to be successful, your moral standard will consist of an objective gauge by which you will be rewarded/punished, likely to have better networking and associates, and other such data by which you can improve personal success. If you primary goal with morals is to maximize the potential success of the human species, then your moral standard should be pretty easy to figure out under an evolutionary/Darwinian point of view. This is pretty straightforward and I don't expect anyone to be confused by this, so I'll quickly move on.
What I have yet to mention is genetic inclinations. I have saved this for last because it is least understood. There is yet to be a complete mapping and explanation of the human genome, so I can't raise evidence such as the selfish gene, or the altruistic gene, or the "benefit to society" gene, because there simply isn't enough scientific evidence to back them up. I can say with moderate certainty that genes influencing the aforementioned qualities actually exist because of our natural inclinations towards not, say, killing every other human being we meet, but I can't be absolutely certain that it isn't wholly a matter of nurture. This is also because I'm simply ignorant in psychology. However I'm fairly sure that there is no black & white answer of nature OR nurture within psychology, because it is reasonably shown that genetics do influence your personality and morals, and that your upbringing and past experiences do influence your morals, but not one or the other. I would include everything I have mentioned earlier as a matter of nurture or experience, but for now I've moved on to nature. What this means to a Theist believing only they are capable of objective morals is that objective morals exist within us even by default. We may not necessarily understand the genes supporting these moral inclinations, but we have almost every reason to assume that they do in fact existence, independent of our implicit visual recognition of them.
Conclusion? Your choice of a moral standards is largely subjective, but the moral standard itself is not unless you fallaciously base your moral standard on preconceived moral or emotional values... in which case I ask - why bother choosing one in the first place? Your decisions are already governed by past experience, your general goal in life, how you empathize with others, and how you wish to improve any of those things. Unless you simply want to put your life goal in words and make it clear to someone else, I see no reason for trying to set your morals in stone and preventing growth unless you really believe your growth is headed in a bad direction.
Thanks to everyone for tolerating the eye-sore that this wall of text has given them, and I really hope that some people are convinced of this and if they already were coming in, to have a more concise and understandable view of morals. Hopefully this isn't a one-sided discussion/debate in which everyone is too overwhelmed by the initial post to say anything other than "Good job" or "I disagree". Not everyone is as comprehensive as INTP/INTJs :p
PS: If you see any grammatical errors, I encourage you to point them out as I'm in the process of trying to improve my grammar.