How do you feel about a Realtor not showing a home because the buyer isn't and wont get pre qualified?

I feel fine about it unless the client indicated they're a cash buyer.  

The difference between a browser and a buyer is that the buyer is willing to take the  basic industry-standard recommended steps that will get them closer to completing a transaction.   If they're not willing to do that, IMO it's reasonable to conclude that engaging an agent is premature.

The agent may lose them (and possibly their referrals), but they may also save themselves from investing a bunch of time in a client that may not be serious, might be a PITA or might not be able to buy even if they wanted to. 

One might even argue that it's kind of rude to parade people through someone else's private property without doing basic due diligence to ensure that there is a valid reason for doing so.

Either way, it's the Realtor's choice and I'm fine with them establishing their own client screening criteria.

I tend to think it's fine in most (not all) cases. One factor that might matter is the realtor's success.  If they're a top 50 in a major metro area, they'd be silly to potentially waste time.  However, if it's someone new to the profession, and/or someone stalled out or in a tough market, perhaps now is not the time to be picky.

Why should they waste their time showing a house that the buyer can’t afford?