How to deal with a clash between paid and unpaid work
For actors it is so often the case that a long spell without work is often followed by an avalanche of opportunities which all come at once. From the bottom of the industry to the top, hot streaks are a real phenomenon and of course these can result in many difficult conflicts. Of course each situation is completely unlike the last and there are no hard and fast rules, but there are a number of things which you should consider when you are in a position where two jobs clash.
It seems like the decision between paid and unpaid work is a no-brainer but spend a moment to weigh up the two jobs, taking finance out of the equation for a moment. Which job satisfies you the most artistically and which will stand you in the best stead in the not too distant future when you are, once again, searching for work. If your only reason for doing the paid job is the money then it may be worth sticking with the other project. If, however, it is an project of equal artistic merit or we're talking about boatloads of cash, then you have a hard decision on your hands.
Obviously, integrity is a great trait as an actor and we all want to keep our commitments. But at the same time, being an actor means selling yourself as a product and sometimes you need to look at it this way. It can be easy to fall into a trap where you are valuing employers more than they would manage you, and you've got to ask yourself if they would be so reluctant to dump you for financial reward.
If you are working under a profit share, then the rest of the cast and crew must also be working under a similar agreement which means they will almost certainly understand when you present your conflict to them. So often actors are incentivised into low or no-pay roles with the promise of exposure and connections that will lead to work so when one such opportunity presents itself then they cannot begrudge you.
Then the two most important factors to bear in mind are time and honesty. Raise your dilemna to your director and explain your problem. As each situation is different, it may well be that you can attempt to work out some kind of arrangement whereby you can fulfil both commitments but it is important to return to time and honesty. Be brutally honest, do you have the time to fully commit to both projects? If not then you will need to inform the director that you are leaving. Some directors may try to guilt trip you out of your decision but it helps to ask where that kind of person will be for you after the show ends. The best way to present the situation to the director is in a timely and honest fashion. The faster you inform them, the faster they can make alternative arrangements. Therefore it is important to be upfront and honest about what you want, the better to reach an arrangement.
An actor I once knew made the last minute decision to ditch a performance he was in, in order to attend a meeting with an agent. He spent the entirety of the run up to his meeting attempting to find someone to take up his role in the play. This was ridiculous as not only was it not his job to cast the play but also he was wasting the director's time by attempting to lessen the blow of the departure. It is not your job to organise things so inform the director of your decision and leave it at that.
Then you should be free to fully commit yourself to the paid work. Congratulations and here's to much more scheduling conflicts in the future!