The most common type of interaction between atheism and theism comes in the form of debates (if people are feeling civilized) or drawn-out arguments (if people are feeling annoyed). Atheism and theism are mutually exclusive options: a person must be an atheist or a theist, but they can't be both and they can't avoid both. At the same time, though, it can't be said that the best option is always unambiguously clear based on the debates atheists and theists have. What's a person to do?
Neither atheism nor theism are choices a person doesn't simply pick one as an act of conscious will. Instead, atheism or theism is usually adopted because of either the force of evidence and reason which a person believes they have before them or simply because that's what they have always believed and it's what they were taught when they were children. Thus while a person may not be able to exercise a conscious choice to switch, they are able to exercise conscious choices which will influence whether or not they switch.
These choices include what sorts of arguments and evidence they read, how strongly they should weigh those arguments, how closely they critique some arguments, and so forth. A person can be held responsible for what they believe because they can be held responsible for these elements that go into belief formation. They can also be held responsible for the methodology the use for weighing beliefs, whether they are consistent and honest in how they evaluate claims, and also whether they spend any time on the issue at all.
Theists commonly insist that their theism and their religion are very important to them, but if that's the case then they should be expected to invest time and effort evaluating their beliefs to ensure that they believe correctly. If their theism and religion are supremely important, then it should be supremely important that they believe in the right sort of god, in the right sort of way, and worship in the way their god expects. Not investing the time and effort to ensure such things is more consistent with unimportant beliefs than with important ones.
The first question should thus not be what should a person believe, but how they should believe. A person should spend time ensuring that they have a sound methodology and approach to belief formation, one that does a good job separating unlikely and untrue beliefs from those beliefs which are more reasonable, more rational, and more likely true. Every day we are faced with a myriad of claims and ideas, not all of which can be true. Indeed, it's likely that more are false than true.
We have an intellectual and moral responsibility to do our best to separate the false from the true. We owe it to ourselves and those around us to learn how to differentiate one from the other and develop beliefs which are more likely true than false. Only by being able to rely on our beliefs and our ability to form true beliefs can we reliably navigate the world around us.
If we can do this (and it's not a task that is ever absolutely complete), then the answer to the question of what we should believe becomes more clear: we will believe whatever their research leads us to see as the most reasonable, rational, and justified position. Once we see whatever is most reasonable, we won't have to do anything to "choose" to believe this we will believe it automatically. If we don't, it's because that isn't clearly the best conclusion from the available data.