Learn Dutch: De fans aanbidden dit model, dus respecteren ze haar imago. - The fans adore this model, so they respect her image.

Dus can act as both a coordinating conjunction (like en or maar) and an adverb. When treated as a conjunction, the word order doesn't change (dus ze respecteren...). However, it is very often used as an adverb meaning 'therefore'. When it takes the first position in the clause as an adverb, it triggers inversion (dus respecteren ze...). Both structures are completely correct.

We use dit for model, which means it's a het-word. Why does the sentence use haar (her) instead of zijn (its) for the possessive?

Strictly grammatically, a het-word should take the possessive zijn (its). However, in modern Dutch, biological gender often overrides grammatical gender when referring to people. Since the model being discussed here is a woman, speakers naturally use haar imago rather than treating her as an 'it'.

Is the verb aanbidden (to adore/worship) separable?

No, aanbidden is inseparable. Even though verbs starting with aan- are almost always separable (like aankomen becoming ik kom aan), aanbidden is a rare exception. The prefix stays firmly attached to the verb, which is why we see De fans aanbidden dit model rather than pushing aan to the end of the clause.