An acquaintance once asked me the following question in an on-line conversation:
“When you tell (your children) about stuff like the priesthood, do you also give them the option to not participate, or to postpone involvement until they receive their own testimony of it? I'm just curious because you seem to be fairly tolerant of unbelievers, and you have a lot of parenting years under your belt (much more than me.)”
I look at things like the Priesthood pretty directly: I believe, and I teach my kids that I believe. For example, all of them have seen the effects of blessings, more than once in undeniably miraculous ways - and I have shared with them experiences with blessings where they weren't involved. I believe they can't gain a real testimony of something unless they experience it, so I encourage them to experience it. When it comes to the Priesthood, I don't want them to "postpone involvement until they receive their own testimony of it", because I don't believe they can gain a real testimony without involvement in it. They might gain an intellectual or vicarious testimony (a belief of some sort), but that's not a real testimony, in my opinion. They have gained as much of a testimony as is possible as a recipient of ordinances (the boys and the girls), but the boys need to be involved on the other end to really understand it fully - just as the girls need to understand their own power through prayer and being in tune enough with the Spirit to give the same type of advice (verbal blessing) that the boys would give in a formal, Priesthood blessing.
Of course, if they don't feel ready for something, I won't push or pressure them into it. My oldest son postponed his mission two years in order to reach a natural break in his schooling, and I wasn't sure for a while if he really would go. It was his decision, and, looking back, the overall timing couldn't have been better.
Finally, as to the "exclusivity" of the Priesthood, I believe it is limited (pun intended) to the areas where the Article of Faith says it's necessary - to preach the Restored Gospel and administer the ordinances thereof. Outside of those specific responsibilities, I don't believe there's one bit of difference in the prayer of the righteous - no matter the religion or denomination or gender of the one offering the prayer. The prayer of faith is the prayer of faith, and God is no respecter of persons.