It may be that they feel that the mission of their employees needs to be in alignment with their organizations mission which is wholly focused around a certain

It may be that they feel that the mission of their employees needs to be in alignment with their organizations mission which is wholly focused around a certain religious set of beliefs. They may feel like someone with a similar mission would be more likely to bring the necessary passion to the job. To quote the bible and Lincoln, 'A house divided against itself cannot stand'... Some women might find it offensive that you compare your religious (or atheistic) beliefs to being a male or a female as one involves a choice and the other doesn't. Being an Atheist will surely limit your ability to have passion for the mission of their non-profit (which also will probably pay less and require more of a personal passion for the job than just a simple desire to make a paycheck), but being female or male shouldn't have an effect on ones ability to do any given job.