Davidson College comes to mind. Moderate but still intellectual engagement and discussion on campus.
@prezbucky, In my humble opinion both Gettysburg and Bucknell would be considered more conservative campuses. Both have large, strong, Greek communities and very conservative alumni. Dickinson might be a slightly more moderate mid PA LAC.
Washington&Lee is considered one of the most conservative colleges in the US (with TAMU).
LMU used to be “not particularly religious” but four or five years ago some alumni complained that it was losing its Catholic character, so now it’s more striking, starting with the supplement, which consists in parsing and commenting Papal quotations. However it IS a good balance.
Some conservative students have an issue with social justice (it’s become a recurring joke for ‘Mil*-fans’) and some Catholic evangelicals consider that Catholics aren’t really Christian, so Catholic schools/students may not be the best choice for OP depending on what OP wants. (social justice used to be a distinctively Catholic way of framing some issues, thus Catholics were the original target of the term before it was broadened to encompass a large segment of typical student protests/agitation.) If OP has no issue, then I agree many Catholic schools should work, although Holy Cross and Notre Dame are definitely on the conservative side.
Possibilities:
Davidson
Denison
Dickinson
Kenyon
Hamilton
Rhodes
Emory’s Oxford
St Olaf
Lafayette
Franklin&Marshall
Whitman
UDayton
Illinois Wesleyan
Butler
Drake
I guess the term “Social Justice” has been co-opted and contorted over the years. I just meant that volunteerism is highly valued at many Catholic schools, esp the Jesuit schools. And not necessarily political volunteerism (although I knew a few students and nuns who were arrested for chaining themselves to defense contractor’s doors, in El Segundo, back in the early 80s!). But volunteering that is directly involved with helping people. Soup kitchens, working at shelters for abused women, tutoring low income primary and secondary school students, etc.
My son applied to LMU and was take aback by the outright Catholic Church-oriented supplemental questions. Hope that does not scare away too many non-Catholics. It would be a big loss for the diversity on the campus. 
At some point you will want to consider intellectualism in general, its various forms, and to what degree you want it to be systemic to your college experience. Colleges such as Kenyon, Hamilton and Williams, for example, may express their smarts in a way that could be different from that at, say, Bucknell or Colgate.
I meant to include schools that have a preppy element and are fairly politically moderate overall (compared to the general population) – or fairly conservative compared to most colleges, but not BYU-or-Liberty-conservative. W&L and Bucknell might be more conservative than I’d thought. They’re still not quite as socially conservative as your average Protestant school, probably. I definitely wanted to stay left of BYU/Liberty in my suggestions. hehe
I think it’s threading a very complicated needle to find intellectually stimulating colleges that have never had discussions that degenerated into shouting matches (Yale), anonymous internet bullying (Williams), newspapers burned (Wesleyan), or instances of mob mentality (Berkeley, Middlebury). We can try to build a case for this or that school being more “moderate” than others, but, when you look under the hood there’s almost always a bigger sports scene, a large pre-professional academic component or just a lot less socioeconomic diversity that partially explains why. Catholic colleges sound fine until you try to get funding for a gay student organization. Life is full of tradeoffs. The OP has to figure out what his or her priorities are.
Actually, the OP is a parent: their student will have to figure out what her/his priorities are 
Social Justice has gone from helping people that need help to beating and macing people who you think you disagree with.
URichmond may be another option for the OP.
One approach I have used is to read posts on threads where the OP is seeking out specific criteria that I know is the opposite of what I know my student wants. Reading those threads and the descriptions provided about schools other posters are recommending and the specifics about their why’s might help you create a list of schools that you believe would not fit your student’s needs. Or it might help you mentally frame a clearer idea of what criteria you are seeking. Sometimes knowing where they don’t want to apply or understanding what they don’t want can be as helpful as where/what they might.
“Social Justice has gone from helping people that need help to beating and macing people who you think you disagree with.”
There is one of those broad brushstrokes again that causes division in this country. Not really needed on this thread nor helpful.
“There is one of those broad brushstrokes again that causes division in this country.” Pointing it out is more divisive than the actual violence?
Focusing on a few isolated incidents (that may not have even been students), on of which was “hair pulling” and using them to mischaracterize entire swaths of higher academia, and holding those isolated incidents as more meaningful and revealing than the centuries of entrenched racist and misogynist violence and oppression, both literal and institutional, is more divisive than those few isolated incidents, yes.