When you're dealing with adjacent independent clauses, you need to consider how they are linked not just mechanically but semantically (that is, in meaning) and prosodically (that is, in the tonal 'shape' of the utterance). Your choice of words indicates the semantic flow, but it must be reflected in the prosody—which in writing is signalled by the pointing.
When the thought of the first clause is directly continued in the second, we join the two with a coordinator, such as and, or, but, so (depending on the sense). The pointing between the two clauses indicates the 'quantity' and 'quality' of pause.
No point would indicate no pause and a continuous 'wave' of rising segments to the end. This would call for conjoining not two clauses but two predicates:
Plastic surgery is ↗vain and un↗wise and should be ↗banned↘.
A comma indicates a brief fall-and-pause before plunging forward. This calls for conjoining two clauses. Your thus (or therefore or consequently) may be introduced in a secondary position to slip in the notion of logical consequence:
Plastic surgery is ↗vain and un↗wise↘, and thus it should be ↗banned↘.
But if you introduce the second clause with thus or furthermore or anything of that sort, you're signalling a new thought moving in a new direction. This calls for a strong fall-and-pause at the end of the first thought, of the sort which is indicated by a semicolon or full stop:
Plastic surgery is ↗vain and un↗wise↘; ↗thus, it should be ↗banned↘.
Plastic surgery is ↗vain and un↗wise↘; moreov↗er, it should be ↗banned↘.