it is a civil offense, like a speeding ticket, $100 fine.  

At that point it's called criminal trespassing.

As pet lovers ourselves, we typically like to meet your pets at some point in the process, too.Our tenants’ safety and the peaceful enjoyment of their home is important to us, so we do a credit/criminal background check on all applicants aged 18+.

Yes, that could very well lead to legal/criminal problems.  

That triggers any clause you have regarding police or criminal activity.

Maybe none of them make enough alone, and they have a reasonably amount of other debt, but together they make more than 5x rent, all credit is great, and no criminal or eviction issues.

And if the community backs him, what are they saying about criminals in general?

Is an LLC actually going to protect me in case of such an offense (I do not intend on performing illegal acts at all)? 

@Sterling WhiteI do not, I am speaking strictly from criminal statistics, and close friends who are police officers in some of those neighbors and some of the issues they deal with.

While credit checks aren't as important though I would still insist on a criminal background check, wouldn't want to introduce people to the neighborhood who are likely to be into criminal activity, especially if they were registered offenders.