Is a cash bar okay for my circumstances?

I've been reading a lot about how cash bars are an absolute sin. My own mother thinks it is perfectly acceptable, but I have read otherwise. I do plan on having a Saturday evening reception immediately following my ceremony and going straight into dinner. The whole reception should end early (around 8pm or so). It is in a private room in a really good restaurant, there will be no dancing. I am getting married quite young (21) and paying for the wedding almost entirely on my own. I am only inviting 75 guests who are all family, no young friends and they skew older. I can't say any of them are big drinkers either. Not having a bridal party as well. We are having a harpist and a cute ice cream truck at the reception. Even if I cut the costs of both of these extras, alcohol would still be at least $700-$1,000 more. Even just having beer and wine doesn't seem feasible and the costs of that are still huge, along with drink tickets. My mother also doesn't like the ideas of a dry wedding. I myself have never consumed alcohol and neither does my fiancé and I would much rather have the things I enjoy. I am having no other events for the wedding like a bridal shower, rehearsal dinner or engagement party that would be an added cost to guests. All guests live in town as well. What should I do?