It truly depends on the market you are dealing with - in a smaller community setting it may be wiser to not come off as unavailable, and to wait and not have too many irons in the fire all at once.
I have over the course of my career had to turn down interviews, interests, contracts, and even had to leave projects mid rehearsal or run. Is it fun to do? No. Is it sometimes necessary when a more appropriate opportunity comes along? Yes.
When turning down an initial offer I keep things very professional and light, thank them for their interest/thinking of you for the position, explain that you are already booked or have accepted other work, and wish them well on their production and that you hope you can work together in the future. In a big market like NYC there are rarely hard feelings to this kind of response, sometimes it ultimately makes them remember you because it is a good sign that you are working
When having to leave a project after already accepting or beginning rehearsals, etc is much stickier and has always been my least favorite thing to do. If you are union it can be as simple as the other job is offering more money (which has been the case with me.) In these cases I have taken time to line up my replacement (or generate a list of suitable replacements) before sitting down with the general manager to discuss my leaving the production. Often this requires a two week resignation, but on a showcase I have left on about 5 days notice due to getting offered a tour. If done tactfully it can be a relatively painless process.
Ultimately in my experience people understand you have to move on/move up to make ends meet or make more money. Without those enticements (as in picking one project over another based on staff, content, etc) it may be harder to come up with a legit out.