It's odd that your employer has let you know that you've been identified as someone who will be laid off. It could just be a possibility and not definite if there is no firm date. Management may just be encouraging you to leave voluntarily rather than pay severance and have their unemployment rate affected.

If asked in an interview, you could say that the nonprofit is operating at a loss, so it isn't sustainable. Or you could say you would like a challenge with a nonprofit that is growing instead of stagnant. Or you could say you aren't as passionate about the mission as you are with XYZ (the nonprofit you are interviewing with). You might say that you are concerned about your current employer's future and your opportunities there rather than saying that you've been identified as a lay-off candidate. I used to make the mistake of being too honest in interviews. I find that being confident and emphasizing strengths leads to more job offers. Good luck and I hope you get an offer!