Integrity
I think you are from a foriegn country, and I'm not sure you use the word "integrity" in the same way we do here in the US. To me, having "integrity" means having good moral character, honesty, etc. I think most card counters have good character, but many do not. In particular, I know of some posters to these sites who are, in fact, con men making their living off of counters, or would be counters, instead of counting. And I suspect there are many more of these that I am not aware of.
Now I think card counting is very moral, because I believe the proliferation of casinos is a "bad thing," at least the way it's evolved in the US. Even if I thought casinos were a good thing, I wouldn't have a problem with card counting; however, I might have a hard time doing it as a full time profession, and I might have a hard time lying outright in a casino "for cover." But since I view casinos as "the enemy," I have no scruples about lying for cover. I think it is similar to lying to your torturers, in time of war, to save your life, or your buddies' lives. However, the lies I tell are not, to my knowledge, harmful to anyone but the casinos. I've never had to "bear false witness against my neighbor."
I go way out of my way to try to be honest to my fellow advantage players, since I think we need that stability. I also tell people , in and out of the casinos, about my losses, but keep fairly quiet about my wins. I think this kind of honesty is bearing good witness, by discouraging people from gambling. I can't think of anyone who needs encouragement to gamble more than they do. I can think of a lot of people who need to be dragged away forcibly from the slot machines and table games.
There is the issue of whether card counting constitutes a productive use of our time on this planet. There are also issues of stability and responsibility -- whether or not gambling is a reliable way to take care of your dependants (probably not) and a good example to set for your children. A lot of this comes down to personal circumstances and what options are available to each individual. Each person must decide for himself whether card counting is a good way to spend their time, here on earth, and how MUCH time to allocate.
Card counting, in itself, isn't immoral, but devoting your life to card counting may well be immoral for most people.
ETF