Examples? There's a discussion of these issues at the "Freakonomics" podcast from Stephen J. Dubner on May 18, 2018. Along with Effron, Dubner also talks with John List, who describes one of his own recent studies.
In that study, workers were hired to transcribe 10 images of about 30 German words each. The workers don't speak German, but they can use Google translate or a similar program. The workers are paid the same no matter the quality of the translation. In addition--and this is the key point--workers can just say if an image is illegible, and they are paid the same anyway. In the experiment, one group of workers were just paid money, while the other group was also paid the same amount of money, but also told that the firm was making a contribution to UNICEF based on their work.
So which group would you expect to be more likely to report that the images were illegible? The group that was just getting paid, or the group that was also getting paid while doing good? List's study found that those who were doing good were 24% more likely to report that images were illegible. Not to put too fine a point on it, those who were doing good were also more likely to shirk or cheat.
There are a number of studies with a broadly similar theme. Here's a samplling
One study done back in 2008 asked whether a white person or a black person would be more qualified for a certain job. They were also asked about whether they favored Barack Obama for president--but some were asked before the question about job suitability and some were asked after. "[T]he opportunity to endorse Barack Obama made individuals subsequently more likely to favor Whites over Blacks." Effron, D.A., Cameron, J.S., Monin, B., Endorsing Obama Licenses Favoring Whites, Journal of Experimental Social Psychology (2009)
Those who "received weekly feedback on their water consumption lowered their water use (6.0% on average), but at the same time increased their electricity consumption by 5.6% compared with control subjects." This finding is noted in Verena Tiefenbeck, Thorsten Staake, Kurt Roth, Olga Sachs, ""For better or for worse? Empirical evidence of moral licensing in a behavioral energy conservation campaign." Energy Policy, (2013, 57, pp. 160-171)/.
When those on a weight-loss are prompted to think about unhealthy eating choices they did NOT make in the past, and thus can feel more virtuous about their past eating patterns, they become less likely to hold to their diet. " The result comes from "The unhealthy road not taken: Licensing indulgence by exaggerating counterfactual sins," Daniel A. Effron, Benoît Monin, Dale T. Miller, Journal of Experimental Social Psychology (May 2013, 49:3, pp. 573-578).
Sometimes just anticipating the prospect of doing good in the future can free you you up to do bad in the present. Jessica Cascio and E. Ashby Plant study "Prospective moral licensing: Does anticipating doing good later allow you to be bad now?" Journal of Experimental Social Psychology (2015, 56, pp. 110-116):
"Across four studies we explored whether anticipating engaging in a moral behavior in the future (e.g., taking part in a fundraiser or donating blood) leads people to make a racially biased decision (Studies 1 and 2) or espouse racially biased attitudes (Studies 3 and 4) in the present. Participants who anticipated performing a moral action in the future displayed more racial bias than control participants. ... These results demonstrate that anticipating a future moral act licenses people to behave immorally now and indicate that perceptions of morality encompass a wide variety of concepts, including past as well as anticipated future behavior."
Here's a comment from Effron in to motivate a 2014 study ("Making mountains of morality from molehills of virtue: Threat causes people to overestimate their moral credentials." Personality and Social Psychology Bulletin, 40(8), 972-985, citations omitted from quotation):
"On trial for ordering the 1995 Srebrenica Genocide, in which thousands of Muslims were murdered, former Bosnian leader Radovan Karadzic claimed that his actions could not be classified as genocide because he holds no anti-Muslim prejudice. As proof, he pointed to the fact that his former barber was Muslim. Many observers were unconvinced; it seems that Karadzic overestimated how much his choice of barber gave him “moral credentials". The present research examines how the motivation to defend against threats to one’s moral character can bias estimates of how others will judge one’s past actions. It is often ambiguous how diagnostic of moral character a particular action is. Does giving a dollar to a homeless person prove that one is generous? Does having a Black acquaintance prove that one is not racist? I propose that people are more likely to think that the answer to such questions is `yes' when they experience a threat to their moral identity—and as a result, they are more likely to overestimate how much they have convinced impartial observers of their morality."
For overviews of research along these lines from a few years back, see "When Virtue Leads to Villainy: Advances in Research on Moral Self-Licensing," by Daniel A. Effron and Paul Conway, " Current Opinion in Psychology (2015, 6, pp. 32–35) or "A Meta-Analytic Review of Moral Licensing," by Irene Blanken, Niels van de Ven, and Marcel Zeelenberg, Personality and Social Psychology Bulletin ( 2015, 41:4, pp. 540–558).
The bottom line here is old and familiar. In a mild form, moral licensing is an issue for all of us. Anyone who exercises hard and then feels that they "deserve" a high-calorie treat knows the feeling. At an extreme form, it is manifest when some of those who claim to be leaders in family values or social justice or religious/spiritual leadership are found to be acting in ways that counter to the values they claim to profess. Such cases may just be hypocrisy, but I suspect there is often an element of moral licensing as well: that is, being identified with doing good can free someone up to do bad, as well.