Translation:Bad people do not respect their parents.
Yes. Usually the members of the family, as well as many objects, are just expected to 'belong' to the subject of the sentence. It's just the case of what is most logical.
This sentence is a bit less usual, so let's look at something simpler.
"Oni kochają mamę" = "They love their mom". It seems pretty obvious that they probably love their own mom. And if by any chance this is not the case here, only then you specify it.
rodzic (parent) is a masculine noun.
Rules for declining masculine nouns in the genitive plural:
"Hard-stem nouns have the genitive plural in -ów: zeszyt notebook → zeszytów. Most soft-stem nouns have -y/-i: hotel hotel → hoteli. Some, especially stems in c, dz, and j, have -ów: kraj country → krajów. All nouns with the nominative plural in -owie have -ów: m husband → mowie, mów."
Swan, Oscar (2008-10-12). Polish Verbs & Essentials of Grammar, Second Edition (Verbs and Essentials of Grammar Series) (Kindle Locations 461-468). McGraw-Hill Education. Kindle Edition.
So it's a totally regular declension here.