This should not be terribly surprising. There doesn't appear to be a big difference in reported moral behavior for the religious from non-religious populations.
What appears interesting out of it so far
1) Haidt's moral framework of distinct moral values and the ideological or religious faultlines over which are held in higher regard is rather clearly demonstrated in what people self-report as moral violations or achievements. Religious (conservative) people often identified different things as immoral than the secular (liberal) population. This probably explains a large measure of why non-religious persons are often regarded as "immoral" by religious people, because they do not identify much of their behavior as morally and ethically questionable where the religious person does. This does not mean that non-religious and secular persons have not considered these questions or that they avoid these moral quandaries in order to do things. Instead it usually means they don't find it very important to judge themselves or others on these questions and may regard them as matters of personal taste; Coke v Pepsi style or rap v country rather than intractable social questions.
2) People report hearing about immoral behavior much more often than moral behavior. This is the traditional transmission vector for morality, getting other people to gossip about your misdeeds. I suspect religious people are more vulnerable to negative gossip (from within "their" group). Most secular persons I am familiar with are vulnerable to negative gossip, but mostly because they may try to ignore it until it has already caused a problem for themselves. Paying attention to the opinions of others is tedious, and often a waste of time, but sometimes carries benefits.
3) Religious people experience more guilt or shame over moral questions. This does not appear to lead them to avoid these actions however. It means they feel worse about it. My off-the-cuff impression is that non-religious people experience less guilt mostly because the moral behaviors that religious persons identify are more common (purity or disgust violations) and easy to identify. Non-religious person's ethical codes are more likely to identify most behaviors that are non-harmful (to others) and consensual acts to be acceptable and experience little guilt over these versus other actions where other persons were harmed, which are less likely to occur or be observed in a daily or weekly pattern. If they feel guilty over drinking too much the night before, it's probably because of the hangover and not because they violated some decree, as an example.