Customer or compliance, which one should get the first priority?

i agree with Gary....its not a chicken and egg problem...and one must ensure compliance with the regulations at all times to serve their customer fairly.
For example, a Bank receives deposit from a customer and give loans another.
Now if we relax the lending requirement and does not ensure compliance to the Bank's internal policy to serve the customer who takes loan, in a way we are putting the money of the depositor ( who is also another customer) at high risk.
Hence, compliance with internal policies and central bank regulation is a must to ensure all the customers are served fairly and uniformly.

compliance first , since any transaction must comply with bank policy and procedure in addition with the central bank of the country

Compliance goal is to finally either serve or protect a customer , Customer is following compliance in all cases since compliance protects customer from general risks, so compliance first.

Regulatory compliance is by definition developed to protect the interests of the customer, shareholders and stability of the financial markets.
If you look at FCA type regulation such as TCF (Treating Customers Fairly) you will see a theme by which the regulators emphasise the need for financial institions to put the needs of their customers first.
By doing so you are implicitly complying with regulation, however, an institutions policies should always reflect, legislation, regulation and entity strategy (in that order).

Customer

Customer

CUSTMER

In reality customer focuss and compliance of rules are not opposite to each other.
Regulations are meant to sfaguard interest of the customers.
Hence, explaination and circulation of regulations needs to be emphasized.
In short compliance of rules and SOPs are must.

compliance coz its thecommand or wish of the customers

Great question, from our basic learning and personal experiences, we all know that customer is the King and should be given the first priority. However in NO ways compromising with Regulatory Compliance / standards.

From Regulatory perspective, zero tolerance to slippage on AML Regulations. All bankers very well aware of that Customer is the ONE, who provides us the business and contribute to the growth of our industry and provide revenues. At the same time, the non compliance or breach of local and international laws would cost a bank its 'reputation' and an hefty financial fine or they may lose their banking license. Hope its clear to all my dear banking colleagues.

In order to maintain the highest reputation of the bank, we should welcome the customers, who respects and adhere to comply with local and international banking laws/rules. 

Compliance First >>> Without compliance with laws, regulations & legislation, there would not be a Company, Corporation,..etc.
and thus there will not be a client / Customers...