This problem in interaction is more a question of distance than of respect, until you can determine that the person that seems not to take into account the notion of distance does that deliberately in order to show some contempt. This may be the case on an initial encounter but it can be very difficult to decide whether this is so; consequently, it is probably better not to take offense too soon, and to do as advised in the comments above (user Barmar), that is, avoid to adopt a similar level of informality; that is a good idea since, in any case, you believe it does not correspond to the situation at hand; in other words, you cannot be reproached with preserving your integrity.
However, you should not take it for granted that your new acquaintance is necessarily fully at ease with a range of behaviours proper in various circumstances, or in other words that he/she is to the manner born when comes the time to use a proper level of formality. It takes some people sometimes a little longer to internalize behaviours that are to them rather unusual, and until they have become comfortable with those, which might, for certain individuals, be never, it is not a negligible imposition on their person to demand of them to adhere to those manners. If the interaction is to be prolonged over a long period, you might just have to be resigned in the thought that your acquaintance is not quite capable of identifying the proper level of formality and/or feels awkward when trying to adhere to manners that aren't quite his/hers, which means preserving your formality while accepting the informal counterpart; I must admit that such an interaction is bound to be found intolerable to many, but the only alternatives are training that person to adopt other norms of politeness or revert to arrangements in which this interaction has no more any reason to exist. Those alternatives, however, are merely theory: it is not much of a problem, in a court of law to whisper into the unknowing witness's ear that he/she should address the judge as "Your Honour", but life is not a court of law.