After teaching at two Catholic schools during my graduate career (one SLAC and one mid-sized research institution), I can ensure you that the department does not care. You will be happy to know that any interview questions regarding religious affilitations are illegal. As an agnostic myself, I have never felt out of place in any environment.
As for what to write in a letter, religion doesn't have a monopoly on moral behavior. The ethical principles we are supposed to uphold as psychologists (e.g., integrity, service to the community, respect for individual dignity, etc.) are on par with any religious faith, so emphasizing these values will be evaluated 'in the eye of the beholder.' It's not fibbing if you express your values and let them attribute them to whatever belief system they like (which we know occurs from basic cognitive psychology).
If you are hired, I do offer one caveat. You can potentially run into problems with students if you openly and antagonistically teach certain perspectives to a student population brought up on creationim. There are a wide variety of religious disciplines (and their accompanying schools) ranging from fairly conservative/fundamentalists to fairly liberal beliefs. So you'll just have to research your student base. I've always found that starting the semester by discussing different modes of knowledge and their independence (specifically, empiricisim versus faith) completely relieves students of any religious defensiveness throughout the course (e.g., discussing research regarding evolution, homosexuality, etc.) and ultimately opens their minds to competing perspectives. That is the point of education after all!