Wedding with no reception

Yes, it would be very rude to have people pay for their own meals. Providing a meal to your guests is your way of thanking them for attending the event you are hosting.

Very rude. If you invite people, you pay.

Yes, that is extremely rude.

The reception is to thank people for showing up for you at the ceremony to support your wedding. It would be rude to not have anything. If you're inviting people you should host something. I would suggest a non meal-time ceremony, like 2 pm, then followed by coffee and cake immediately afterward.

You can possibly mix together the pay-your-own-meal with Jacks' recommendation. You really need that reception with some snacks or desserts. You may be able to do this at park or community center. If a small enough crowd, maybe at a home. This allows the guests to meet the newlyweds and share a bit of time together. You might also do a cake cutting or have a few toasts (even with apple juice).

After that event, it may work to have a restaurant as an informal gathering. People do have to eat. Hopefully, this is not seen as an insult to guests only figuring there was a reception. But you have shown this is only for family.

Definitely do as others are suggesting and just do a “cake and punch reception” where you have light refreshments. You don’t even need a cake if you don’t want. Have your ceremony during a non-mealtime and put something like “light refreshments to follow” on your invitations. That will clue your guests in not to expect a full meal.

That's very rude. If you don't want a large reception, have your wedding at 2 and just serve cake and punch.

Adulting is paying for your own wedding. Otherwise you're charging guests for entry into a "show". Come up with a plan with your partner to save X amount each month.