As a customer service advisor, would I have any dealings involved with interest? I.e charges that have interest fees

Given the nature of how the tax system works, interest is an integral part of most compliance or customer service roles. Anyone working in those roles would need to deal with late payment and repayment interest when it arises. I don't think it would be considered a reasonable adjustment not to have to deal with interest in those roles, given the frequency and unpredictability of when it would arise. I'm aware that many Muslim colleagues work in such roles and, presumably, deal with interest. However, if your personal faith means that you can't do that, there are roles in HMRC that don't involve dealing with interest. I'd suggest having a conversation with your manager to explain the issue and explore a move that would meet your needs. 

Depending on the role you work in you may not have to handle interest at all. I'd recommend checking through what is entailed in the description of any job you apply for first and at the bottom of the application form there is also usually an email address for the person advertising the role. You could always see if you can contact them to gain a little more understanding of what you would be expected to do in the role.