"Has anyone else been dancing for a while and found it difficult to make friends? Sometimes I feel like all of the relationships I have developed through dancing are very shallow. One of the main reasons I got into dancing was to try to meet girls and make friends, but it almost seems counterproductive after I've been in it for a while. "
It may be that dancing is the only way in which you as a person overlap with most of the people who you encounter in the places you are dancing. Dancing can really open some people up, but it may not change who they are as a person. If you are in a room full of people you would not have any other reason to be friends with, the mere fact that you both dance might give you one thing in common (assuming your idea of dancing has much in common - which is not a safe assumption) but it may not give much depth.
Dancing often gets "sold" (and I mean promotion from other participants as much as lesson marketing) as a "solution" to many things. That often results in unrealistic expectations. Occasionally it has great benefits, but mostly people are still the people they were before, just a little more active, perhaps a little more confident, and with a fun new skill.
Another possibility worth considering is if you are dancing in the wrong place (for you), one that does not attract the kind of person you would naturally enjoy a friendship with. There might be a venue with a clientèle you would be happier to be a part of, or there might not. Unless you have very possessive studio managers, you should even be able to study in one location if the instruction is best, and enjoy dancing in another if the crowd is best.