I assume by messy you mean that you don't yet want to confront the issue of your non-belief with your parents, especially since you still live with them.

I was put in a similar situation with my parents as well. They would find matches through friends and family and each time I visited I would get pictures and information about some girl who was marriageable. It was easy enough to shrug them off and seem disinterested but as time went by I felt more and more pressure to "just talk to them" as my parents said. What would be the harm in having dinner at her parent's house in a month or two they said? Like you, wanting to keep my parents at bay I eventually obliged and agreed to visit a girls house. I thought it would be easy enough to wiggle out of awkward decision as I had been doing for years. The problem was that the initial visit is actually somewhat of a commitment to at least seriously consider marriage. Since dating in the Western sense is forbidden, the initial house visit is essentially the first date. Their parents were (as my mother later explained) gracious enough to even let me speak face to face with their daughter. Despite my parents pressing, I managed to convince them that it was not a good match. I cited fabricated differences in personality and career trajectories and managed to weasel out of it. This was not before a long lecture about wasting people's time and how I brought shame to the family by going to their house and cavorting with their daughter!

Now I don't how conservative your family is, or how useful my experience may be to you if we have cultural differences but I can only advise you to not meet any girls if you are not seriously interested in marrying them. I know you said you don't believe and if that also means that you do not wish to marry a muslim girl then you really shouldn't be talking any muslims girls your parents are trying to set you up with. The girls are likely to be serious about marriage and it is not fair to them to let them think they have a shot with you.

The legitimacy of an arranged marriage is easily evaluated in modern Islamic culture. You need a resume and headshot to gauge interest, then if during a brief conversation you do not abhor this person and have similar goals the understanding is that the rest is left to Allah and you should go for it. For this reason, that first house visit is all your parents think is necessary to essentially decide if you want to spend the rest of your life with said person. I've been there before, how can you say no if all the possible ways to analyze this marriage has been completed?? So again, do not agree to open up any sort of interaction unless you are actually willing to get married.

For some more relevant advice, you could say that you are going back to school soon and would to think about marriage later. Or that you are not quite ready for marriage yet, or that you wish to save more money for dowry/marriage/ring/etc. You could also say something struck as odd about her father/mother/brother etc. Do what you need to do to wriggle out this, deal with your parents disappointment and make sure it doesn't happen again. You'll need to deal with a more long term solution eventually, as this won't just go away. Good luck.