I want to say "the reality of and outlook on crime in Europe" without using two prepositions.
Can I say "the reality and outlook on crime in Europe?"
Can you lead me to a grammatical reference for this issue so I can read further?
When forming a parallel construction such as this, it is important to include all the words necessary to make the parallelism work properly. Since, as you note, "outlook" and "reality" require two different prepositions, those prepositions need to be included in the paralleled structures. However, the prepositions do make the sentence look at least a little bit awkward, so it is probably worth your while to search around a bit for alternative words that use matching prepositions, or to reword the sentence to eliminate the parallel construction:
First, what do we mean by "outlook?" Prediction? Opinion? Emotion? The word tells us very little. Better to use a word that's not so lazy, not so weasely. Also "reality": why not just say or show the facts without the preamble?
Then, to me, the reality of crime and the "outlook" on crime are two ideas different enough that each deserves its own phrase or sentence:
"We issued 42 speeding tickets last year1. We are working to cut that number by half2."
1 The reality.
The answer to your question is no, I'm afraid you can't do that without sounding odd. Reality and outlook take different following prepositions, and trying to make them use just one will at best jar. The best rephrasing I can think of that keeps your word choice is
That's not exactly wonderful though, and your original phrasing is just fine as far as I'm concerned.