It can be dizzying! The key is to determine what the subject is.
Prepositional phrases do not change whether a subject is singular or plural (Rule #5).
(Prepositional phrases are never the subject, either.)
Once you determine what the prepositional phrases are, you can disregard them for determining what the subject is. Based on the subject, you can determine what the verb should be.
The loss (of [tastes and cultures]) animates ... (Rule #1)
Subject: loss (singular)
Object of Preposition: [tastes and cultures]
The loss (of tastes) and the loss (of cultures) animate ... (Rule #3)
Subject: "loss and loss", (a compound subject, which is plural)
Preposition #1: of
Object of Preposition #1: tastes
Preposition #2: of
Object of Preposition #2: cultures
The loss (of the culture) animates this movement. (correct)
The loss (of the culture) and the loss (of taste) animate this movement.
(subject is "loss and loss", plural)
The loss (of jobs) animates this movement.
(subject is "loss", singular, not affected by the prepositional phrase "of jobs")