No, its not. Here is an analysis of your sentence:
- Mensch und Familie
Man/human/person and family
This is an enumeration with two elements which are joined together by the conjunction »und«. The whole enumeration is the subject of this sentence. The subject names who defines, sets or specifies something in this sentence.
- legen ... fest
defines/sets/specifies
The separable verb »festlegen« is separated in this sentence. I means to define, to set, to specify. Since it's the verb, it's the ruler of this sentence. Everything else in the sentence is somehow connected to this verb.
- in den meisten Fällen
in most cases
This is a prepositional phrase that is used as adverbial clause of frequency. It tells how often something is defined, set or specified.
- nach individuellen Vorlieben
according to individual preferences
This is a prepositional phrase that is used as adverbial clause of manner. It tells under which conditions something is defined, set or specified.
- Regeln zum Gebrauch der Strassen- oder Hausschuhe
Rules for the use of street shoes or slippers
This nominal group is the accusative object of the verb »festlegen«. It names, what is defined, set or specified. The core of this nominal group ist the noun »Regeln« and »zum Gebrauch der Strassen- oder Hausschuhe« is an attribute that further specifies the core of the group. This attribute is a prepositional modifier who itself again has an inner structure, but that is already beyond the scope of your question.
For you important is, that each prepositional phrase and each object needs a core and this core must be either a noun or a pronoun. If the word »Vorlieben« was not a noun, then the prepositional phrase »nach individuellen Vorlieben« would have no core, which is not allowed.
Adjectives can be used in three ways:
- As an attribute of a noun. In this case it stands left of a noun and is declined.
Das rote Auto war teuer und fährt schnell.
- As predicative. In this case the verb must be a copula (like "sein = to be, werden = to become, bleiben = to stay") and the adjective is bound to a noun via this copula verb. So it still describes the property of a noun.
Das rote Auto war teuer und fährt schnell.
- As adverbial. In this case the adjective is an attribute of a verb. So it no longer describes a noun but a verb.
Das rote Auto war teuer und fährt schnell.
The word Vorlieben has none of these functions, so it can't be an adjective.