The usual ones: effective policing and punitive justice. It works pretty well actually if your goal is to keep law-abiding citizens safe without much regard for the fates of criminals.
Policing and crime are fundamentally local concerns. The main predictor of exposure to crime or likelyhood of police encounter is zip code. Some (local) policies are more effective at crime reduction than others. Among the most famously effective is the broken windows theory of policing. The basic principle being that arresting and confining antisocial people is an effective method of maintaining social order and stability. I'm not saying these ideas are "Republican", only that they are "conservative" in the sense that we've been practicing them for milenia.
Can you name any policies or bills that Republicans have to make this happen? Can you prove that social norms have an effect on crime or homelessness? Are you claiming gay people are more likely to be criminals because they don't?
Homeless:
"Research shows that, compared to homeless families, homeless single adults have higher rates of serious mental illness, addiction disorders, and other severe health problems."
How would social norms fix that? If an adult has a mental illness and can't afford care are you willing to have universal health care? You don't think if they had family that could take them in and they were willing they would do that?
"Promoting strong family structures and communities"
What does this actually mean in practice? This vague comment could mean anything from running for office, passing no laws and shouting "Hey don't get divorced" to passing laws making it illegal for anybody to get divorced.
"Supporting social norms that dissuade destructive behavior"
Nobody is for "destructive behavior". What is "destructive behavior" and what changes does this vague comment mean in practice? It could mean anything from passing no laws and shouting "don't do drugs" to dissuading homeliness by throwing all homeless people in jail.
> Promoting strong family structures and communities.
That's not actionable. What does that even mean? What law or laws would you want proposed and passed that would accomplish that? Are there any political candidates that have a list of these laws, justifications -- with hard data -- why these sorts of laws will fix the stated problems, and a plan to get them put into place?