Well it's not entirely clear that it's just related to gambling - Betfair, the UK's largest betting exchange, do all their merchant transactions (customer deposits and withdrawals) through RBS as well - given they're directly linked to credit cards the risk of chargebacks etc. is clearly higher than a day-to-day business account that is mostly used to pay employee salaries (as presented in the article, Smarkets client funds are ring-fenced in a Maltese bank). The obvious difference to me is that Betfair is a multi-million pound company and Smarkets isn't.
Honestly, this is sufficiently and irritatingly common that unless you've talked to the people at Betfair and gotten them to agree with your story, I not only am going to have a hard time believing your take, I'm going to have a hard time not negatively judging your company for telling it like that. :(
What makes gambling low profile ? Its a business, that has a unique model that turns a good profit. Why should it be treated differently from any other startup?
A lot of people have the opinion that gambling does not produce "value", and that it makes people addicted to it, while running them into the ground financially.
I'm not sure about the rest of Europe, but here in The Netherlands it's not even allowed to start a gambling site, as the state has an absolute monopoly on it (Holland Casinos).
My understanding of the reasoning behind this is centred around morality, although I imagine there's also a financial incentive for the state to maintain this control.
There, I've correct that for you :)
Personally, I think it should be obvious to everyone that gambling is a rather low profile business and anyone who decides to do business in such an area should be prepared for obstacles like this; I don't see how running to the press would help at all when the public opinion about your industry is not exactly very high.