I generally say that I've been poly all my adult life. My experience with polyamory started when I was 15 when my girlfriend had a boyfriend. Every relationship I've had since has either begun or become poly. I didn't know the word polyamory until I was in my thirties.
I fantasized about my mom and dad getting a wife so my mom wouldn't be so lonely when my dad was away in the army. I also thought that if one mommy was good, two would be even better. The idea of having both a husband and a wife sounded great to me before I ever even thought about sex. I had romantic crushes on couples starting in late grade school, particularly my science teacher and her husband.
I think that people mean they've been poly for the entire time in their lives when they've thought about romantic relationships when they say they've been poly all their lives.
I didn't listen to the Minx but I have run into this attitude before. The rationalizing of an activity and trying to fit it into an unrational belief or world view. What you have is someone trying to understand themselves inside the trappings of religion. I think for most people the idea of no god or religion is so far beyond what they can understand so they try to find justification in what they do from god or inside their belief.
Personally I think they have no integrity. If you believe something, live it. If you don't believe it, find out what you believe and do that. I don't think they are being honest with themselves and are not willing to look inside and be honest with what they see and feel.
I love polyweekly, and Minx is a sweetheart, for someone like my self who is addicted to podcasts it is an invaluable source of information. she has had some fantastic guests who talk about religion in poly. There seems to be a lot of...if not organized religion then perhaps spiritualism within poly that for me can be off putting. One of her reoccurring guest and occasional co host is Joreth (http://www.theinnbetween.net/) she is an atheist as well as poly, and has a great perspective on the community and the mono/poly debate.