There are two schools of thought about that. On the one hand you might be more likely in some cases to be asked to play some kind of a role like buddy up with a rookie diver or follow on behind a group to sweep up stragglers if you show a DM or an instructor card. In those cases you're welcome to either accept or refuse depending on your disposition but some people find being asked to contribute to a dive so annoying that they lie about their qualifications in order to avoid the question.
The other thought that I think you need to consider is that *IF* something happens your pockets may not look "zipped shut" to a liability lawyer if you deliberately mislead the dive team as to your qualifications. In accident I can see a lawyer making that claim that if you hadn't lied that that dive team would have made other decisions and that the accident wouldn't have happened, essentially blaming your lie for causing the accident, even if it has nothing to do with it. Remember, lawyers don't care what really happened, all they want is to be able to nail someone for it.
That second bit is why I never lie about my qualifications, and to be honest, while it has happened from time to time, I've never felt that a dive crew asked me to do something that would have caused a conflict if I had declined.
R..
This has been discussed frequently. Here is my take.
In recreational diving situations, I always show an instructor card. I have never been asked to do anything described above, and I don't know anyone else who has either. In fact, it is quite the opposite. An operator with multiple boats or groups of divers will put me with the best group doing the best dives. For example, I was once on a boat with more than 20 divers in Hawai'i. We were divided into three groups. Two groups were raw beginners. In my group, we were told that every diver had at least 500 dives, and you can believe we were treated very differently from the raw beginner groups. In the raw beginner groups, there may have been some professionals who had smugly refused to show their highest card so that they wouldn't be paired with beginners. I don't know.
Not only am I regularly placed with the more advanced divers, I am given a lot more freedom and benefit of the doubt during the dives. I get to participate in collegial discussions with the staff. I get other considerations, including occasional discounts. I have never had the slightest regret about showing that card, and I have received a slew of benefits.
In general, dive operators want professionals to be happy. They want them to return, and they want them to recommend them to students. The last thing they want to do is piss them off by sticking them with a bad dive.
The only time I ever performed any professional duties on a dive were at my suggestion. At the end of a week of diving, I had gotten to know the people pretty well. They had a popular dive coming up, and one of their crew could not make it. They needed another professional in the water to meet their insurance requirements. I offered to fill that role, and they compensated me for it. If I were ever to be asked to work in any way as a professional, which I consider highly unlikely, I would demand compensation.