Bali is just one of the 34 Provinces of the Republic of Indonesia and has no special status. Any Indonesian can open a trade in Bali and any Balinese can do similar in any other Province.
Employees from different parts of the Republic, who have a KTP in their home area, need to get a Kipem if they wish to live/work in another area.
Investment from foreign sources is part of the economy of RI. The present government has many times indicated its desire to increase foreign domestic involvement and is constantly attempting to ease the rules, albeit too slow for some, to expand foreign investment.
Supporting local business therefore means supporting the Republic's economy at large and isn't unique to Bali. Even large offshore corporations have to have their PT in Indonesia.
I have a friend who sells Bali carvings, Lombok textiles and Ambon cloves from a store in Jakarta. I've seen many stores in Bali sell culture products from Papua and foods from other parts of the archipelago. There are many Joglo's and Batik made in Bali which are actually native to Java.
VAT taxes generated from any purchase go to the central gov't in Jakarta as do income taxes and business taxes. The central gov't then distributes back to the 34 Provinces according to budgets.
To say a bank is uniquely Muslim or Hindu I would think hard to define. Nearly all banks, excluding those practicing Sharia or Islamic Development banking, are multi-culture/religion/public/private. There are Regional Development Banks (BPD) that are authorized by the federal gov't to offer, as the name suggests, loans for regional development.