Cash bars are not okay at weddings. Inviting a guest to your wedding means that you are hosting them—as in, treating them—the entire time. You aren’t asking them to pay for their dinner, so you can’t ask them to pay for their own drinks.
If you’re on a tight budget, you do have some other options. Remember that what you serve at your event is ultimately your decision, and it’s fine to forgo liquor—it’s not required that you provide it to guests. You could also choose to serve only beer and wine, or even just champagne. Many couples are going with a signature cocktail: One mixed drink that is served to everyone, usually with a choice of beer and wine, as well. A tip to get the most out of alcohol if you do choose to serve it: Ask your bartender to measure drinks, rather than eyeball them. This tends to use less alcohol (and thus less bottles), saving you more.
From The Emily Post Institute