Date: May 22, 2017 05:55PM
1. While what you wrote seems implausible, I do think that bishops delay recommending prospective missionaries if they are struggling with anything that makes their mission success problematic. If he can't follow his parents rules, he's unlikely to be more successful with the mission rules. Did he actually graduate (that is required to be recommended)? Has he really decided for himself to go? Only those who can say yes should be going. There is no stigma for not going at age 18 (and it is entirely possible that he is sexually active with your daughter and whether he has told the bishop or not, that is what is keeping him. Frankly, it would be pretty normal with any adoptee who feels a safe harbor and love for another and is afraid to let them go.)
2. There are lots of children who need temporary or permanent homes. Members who foster and adopt generally see it as an extension of living a Christlike life.
3. While Mormon families have some better success at keeping their kids close to their religious faith than others (see Pew research), lots of mormon youth are not actively involved in the church and/or doing lots of things inconsistent with their faith. Others should not construe the physical distance from the church as lack of belief. Mormon families believe their children who are baptized will be with them throughout the eternities if all live like they should and submit their will to Gods to the best of their personal effort. So they worry greatly about children who stray or sometimes even if they practice the Mormon faith differently that the way their parents do. It is more likely the family will be in an extended state of drawing him closer (and irritating him greatly in the process) than throwing him away.
4. If he has been taught faith and lived in a family that tried to live godly lives, your daughter has nothing to fear from that. Some here might argue that he may have absorbed patriarchy ideas, but there are plenty of mormons who would tell you that their own homes are pretty egalitarian and dads do as much housework and child care as mothers (especially when both are working). So get your kiddo the https://deseretbook.com/p/300-questions-lds-couples-should-ask-before-marriage-shannon-l-alder-50863?variant_id=51843-paperback
and suggest that they are questions that will help her get to really know him and that would be important thing to do. Tell her there are secular versions too online and otherwise if she'd rather use them, but that it is really important in making friends, especially in those they are considering or being intimate with to work alongside their significant other, to do new things neither has ever done before, to serve others, to be with extended family in the ordinary things of life like painting or spring cleaning, or fixing the lawnmower or digging out the tree stumps, like reading and talking about books, like taking younger kids to a museum or parade, like fixing food for the family, or singing at the assisted living center.
Bottom line is that how difficult or enriching his beliefs will be to their relationship is really dependent on what he believes and how he practices his faith, more so than Mormon doctrine itself: no one makes church members do any of the huge number of things they are taught to believe or invited to do.