I've been waffling about this for years (e.g., here and here). Today, I'll try out a multi-dimensional answer.
1. My first thought is that it would be unfair for us to hold ethics professors to higher standards of personal behavior because of their career choice. Ethics professors are hired based on their academic skills as philosophers -- their ability to interpret texts, evaluate arguments, and write and teach effectively about a topic of philosophical discourse. If we demand that they also behave according to higher ethical standards than other professors, we put an additional burden on them that they don't deserve and isn't written into their work contracts. They signed up to be scholars, not moral exemplars. (In this way, ethics professors differ from clergy, whose role is partly that of exemplar.)
2. Nonetheless, it might be reasonable for ethicists to hold themselves to higher moral standards. Consider my "cheeseburger ethicist" thought experiment. An ethicist reads Peter Singer on vegetarianism, considers the available counterarguments, and ultimately concludes that Singer is correct. Eating meat is seriously morally wrong, and we ought to stop. She publishes a couple of articles, and she teaches the arguments to her classes. But she just keeps eating meat at the same rate she always did, with no effort to change her ways. If challenged by a surprised student, maybe she defends herself with something like Thought 1 above: "I'm just paid to evaluate the arguments. Don't demand that I also live that way. I'm off duty!"
[Socrates: always on duty.]
There's something strange and disappointing, I think, about a response that depends on treating the study of ethics as just another job. Our cheeseburger ethicist knows a large range of literature, and she has given the matter extensive thought. If she insulates her philosophical thinking entirely from her personal behavior, she seems to be casting away a major resource for moral self-improvement. All of us, even if we don't aim to be saints, ought to take some advantage of the resources we have that can help us to be better people -- whether those resources are community, church, meditation, thoughtful reading, or the advice of friends we know to be wise. As I've imagined her, the cheeseburger ethicist shows a disconcerting lack of interest in becoming a better person.
We can run similar examples with political activism, charitable giving, environmentalism, sexual ethics, honesty, kindness, racism and sexism, etc. -- any issue with practical implications for one's life, to which an ethicist might give serious thought, leading to what she takes to be a discovery that she would be much morally better if she started doing X. Almost all ethicists have thought seriously about some issues with practical implications for their lives.
Combining 1 and 2. Despite the considerations of fairness raised in point 1, I think we can reasonably expect ethicists to shape and improve their personal behavior in a way that is informed by their professional ethical reasoning. This is not because ethicists have a special burden as exemplars but rather because it's reasonable to expect everyone to use the tools at their disposal toward moral self-improvement, at least to some moderate degree, or at least toward the avoidance of serious moral wrongdoing. We should similarly expect people who regularly attend religious services to try to use, rather than ignore, what they regard as the best moral insights of their religion. We should also expect secular non-ethicists to explore and improve their moral worldviews, in some way that suits their abilities and life circumstances, and apply some of the results.
3. My third thought is to be cautious with charges of hypocrisy. Part of the philosopher's job is to challenge widely held assumptions. This can mean embracing unusual or radical views, if that's where the arguments seem to lead. If we expect high consistency between a professional ethicist's espoused positions and her real-world choices, then we disincentivize highly demanding or self-sacrificial conclusions. But it seems, epistemically, like a good thing if professional ethicists have the liberty to consider, on their argumentative merits alone, the strength of the arguments for highly demanding ethical conclusions (e.g., the relatively wealthy should give most of their money to charity, or if you are attacked you should "turn the other cheek") alongside the arguments for much less demanding ethical conclusions (e.g., there's no obligation to give to charity, revenge against wrongdoing is just fine). If our ethicist knows that as soon as she reaches a demanding moral conclusion she risks charges of hypocrisy, then our ethicist might understandably be tempted to draw the more lenient conclusion instead. If we demand ethicists to live according to the norms they endorse, we effectively pressure them to favor lenient moral systems compatible with their existing lifestyles.
(ETA: Based on personal experience, and my sense of the sociology of the field, and one empirical study, it does seem that professional reflection on ethical issues, in contemporary Anglophone academia, coincides with a tendency to embrace more stringent moral norms and to see our lives as permeated with moral choices.)
4. And yet there's a complementary epistemic cost to insulating one's philosophical positions too much from one's life. To gain insight into an ethical position, especially a demanding one, it helps to try to live that way. When Gandhi and Martin Luther King Jr. talk about peaceful resistance, we rightly expect them to have some real understanding, since they have tried to put it to work. Similarly for Christian compassion, Buddhist detachment, strict Kantian honesty, or even egoistic hedonism: We ought to expect people who have attempted to put these things into practice to have, on average, a richer understanding of the issues than those who have not. If an ethicist aspires to write and teach about a topic, it seems almost intellectually irresponsible for them not to try to gain direct personal experience if they can.
(ETA 2: Also, to understand vice, it's probably useful to try it out! Or better, to have lived through it in the past.)
Combining 1, 2, 3, and 4. I don't think all of this fits neatly together. The four considerations are to some extent competing. Should we hold ethics professors to higher ethical standards? Should we expect them to live according to the moral opinions they espouse? Neither "yes" nor "no" does justice to the complexity of the issue.
At least, that's where I'm stuck today. I guess "multi-dimensional" is a polite word for "still confused and waffling".
[image source]