That's one of those "it depends" questions.Are interpretors allowed to "pick and choose"?
First of all, there are different kinds of interpreters in the decision making process. Private practice/freelance interpreters and those who work for agencies.
Private practice terps make their own assignment decisions. Even then, if the private terp has a contract with a client, then that contract must be fulfilled.
Terps working for agencies often are bound by whatever their contract calls for. Some agencies allow a terp to turn down a maximum number of assignments per year (say, three) for whatever reasons. Then, the agency itself can also turn down assignments from clients for whatever reasons they so choose.
Of course, the terps and agencies that turn down the least potential work get more work in the long run, so it behooves them to not turn down many assignments. The most common reason for turning down assignments is unavailability of terps. Sometimes there just aren't enough terps to go around at that time.
There's no need to "fib" (lie) or make up excuses. One can be truthful without elaborating....If one was called to interpret at this Nudist Camp, and did not want or refused to go...what's gonna happen there? Of course, they could "fib" and make an excuse....
Same as for religious ceremonies...do they call an interpretor of the same Faith?....Even protest rallies (if the Interpretor does not agree with what they are protesting, and feels it might become violent)?....refuses to go?
As far as legal rights, the ADA is specific about the circumstances for which a terp must be provided. It covers most areas but there are still some areas for which a business or group may be exempt. Some exemptions are the size of the organization, or religious organizations.Personally, I'm not about seeing nudie people at a beach or a ceremony or whatever. I'm not an interpretor, but what are their rights? I know we deafies have a right to a interpretor...but what about the Interpretor's rights too?
Certified terps also have some protection under the RID code. (Please see the link I posted.)
Also, there are specialized fields of interpreting that even generally certified terps aren't qualified to do. Even if they are legally allowed to do that kind of interpreting, professional terps know their limitations and will turn down work for which they aren't qualified.