I largely agree with you, but I'm not convinced it's a solveable problem, and you've kind of subconciously noted the problem with enforcing that strictly in your own post - what if someone has strong political views that most people find abhorrent, but the bank has to serve them anyway, but that person is also likely to get them in hot bother because they engage in money laundering, or because they simply cause the bank to take a loss? Can they close the account down?
If no, then what happens when everyone whose causing the bank a loss simply declares they have strong political views and uses that as a shield, causing the bank to collapse?
If yes, then what's to stop them just using that excuse to censor anyway - "Oh they're a fraud risk", or "Oh, they're not profitable enough", or "Oh, they cause reputational damage to the company causing a loss for us".
I absolutely agree with you that financial censorship is scary, whatever one may think of Wikileaks (I don't really like it nowadays, it's become a propaganda organisation rather than a transparency organisation) I thought it was always rather disturbing that the US tried to shut down the Iraq/Afghan war log leaks by strongarming Mastercard, Visa, Paypal et. al. to not work with them to censor them and send them offline. It's definitely a real concern, but on the same note how do you implement that legislation whilst also allowing such organisations to reasonably run their businesses?
Also, should it apply to just banks, all financial organisations, or every organisation? If it's just banks, then that means organisations like Paypal, Visa, and Mastercard can cut them off, if it's all financial organisations that's much more clear cut, but it doesn't change the fact other organisations can still censor - a communications infrastructure company could still choose to cut off their broadcast, so you could apply it to every organisation, but then you're right back to square one where businesses are having to potentially serve people that cause them loss and end up going out of businesses anyway.
Here's a semi-related thought experiment from the UK's recent Brexit vote, in the UK it's illegal to discriminate against employees based on political views, but, if a company is forced to make cuts due to Brexit, then shouldn't a company be allowed to fire those who voted for it first and foremost over those who voted against it? Why should some suffer for other's decisions when it would be fairly trivial to make people accountable for their own actions in this sort of case? Should people really be protected from facing the consequences of their actions, whilst expecting others who aren't responsible for their actions to suffer the consequences instead?
I don't know, or even pretend to know the answer to any of these questions - I'm just making the point that it's massively complex, and I'm not sure there really is a rationally objective answer. I think the answer is always going to be subjective and therein lies the problem - what you may view to be a reasonable approach may not be acceptable to the majority. That is unfortunately the reality of democracy, minority viewpoints often get fucked, and the sad reality is that many people don't actually have too much of a problem with censorship, as long as they're not the ones being censored - they're just too dumb to realise that one day it could be them.