I know it can be done... having a vegetarian meal as a die hard meat eater. my fiancee is ridiculously "meat n potatoes" and the vegetarian places I've taken him to have ended up on his favorites list.... but we're on a TIGHT budget and the really flavorful fancy stuff just ain't gonna happen. In fact were bordering on doing hor d'oeuvres only to try and save. We found a place that offers a decent selection of vegetarian plated options and they're willing to work with us if we have suggestions. I'm trying to get input bc he's ok with going vegetarian (and financially it works great to stay in budget) but I'm getting push back from family. Has anyone successfully worked a vegetarian wedding n shut up the critics? Or are we being "unreasonable?"
Side note: This is our second wedding (for each of us) and it's a celebration for US this time around. (Especially since we're financing the whole thing and only asking for company, NO gifts.) So we feel like all bets are off here. As in dont bother us with obsessive etiquette, we've done the classy thing with our 1st weddings.

Re: Vegetarian wedding
You can serve any kind of food your would like to provided it is appropriate to the time of day. A few passed apps over the dinner hour wouldn't work but you could certainly do that between meal time hours.
If the majority of your guests are vegetarians, an all vegetarian meal would make sense. If you are going all vegetarian to save some money, see if there is something else you can cut to offer some sort of protein. Not a requirement but considers your guests who may be used to eating an animal protein at meal times.
Note - you cannot say "no gifts" on anything wedding related. If someone asks, let them know that you don't require anything and are just looking forward to joining together with friends and family to celebrate. You should never expect gifts so saying no gifts basically says that normally you would be expecting but don't want anyone to bring gifts.
Classy thing vs. whatever you are doing this time around doesn't mean etiquette has less of a place. Etiquette is to ensure that you are thinking appropriately and considerate of your guests. The type of event, casual vs. formal doesn't matter.
As long as you have enough food for the time of day you should be okay. Watch out for hor d'oeuvres. They can be sometimes MORE expensive because they are more time consuming to make. Labor = more money. Not always, but can be.
Since you are are on a limited budget why not try a brunch or lunch time wedding? They are often less expensive.
Gifts are never to be expected, so no need to mention no gifts.
That said, all vegetarian is fine as long as there's a good variety of food and enough for the time of day. If any guests have allergies or health-related diet requirements, those needs should be met.
That said, if you want to avoid people complaining to you after the fact, you may want to have available at least some vegetarian foods that would be familiar to everyone, such as eggplant parmesan or pasta dishes. That way nobody can complain that you that you had all "weird" food.
One thing to think about, you say your FI is ridiculously meat and potatoes, does he actually want a vegetarian wedding? You may want to price it out but I'm not sure strict vegetarian options are going to be cheaper (they weren't at my venue).
If not, talk to a Italian restaurant- even Olive Garden or Maggianos. Eggplant Parmesan, spaghetti with marinara and buffalo mozzarella, cheese/mushroom ravioli are all nice choices. Salad, breadsticks, apps like brochette and cheese and crackers are all tasty and inexpensive. Stay away from "fake" meat like tofu meatballs.
That being said, have you thought of doing a late evening, dessert-only reception? Get married at 8:30pm and then serve lots of different cakes/ /desserts along with some simple veggie and cheese trays? If you are so concerned with a vegetarian meal, and budget is an issue, most people wouldn't even notice a dessert reception that was vegetarian.
It's fine to serve a completely vegetarian meal. You don't need to run your menu by your guests for approval. But you don't need to be a rude host.
You can still have an "US" wedding and follow basic hosting rules. If that means having a vegetarian menu, then have a vegetarian menu. No one is stopping you. Just stop asking for your family's input if you are going to do whatever you want anyway. That's like when your friends say "where do you want to eat?" and you're like "I think La..." "OK well I want Qdoba." Why ask, you know?
Pick a couple of heavier vegetarian dishes like vegetable lasagna, mushroom risotto, vegetarian pot pie...you get the picture.
If you're on a tight budget, heavy apps may not be any more economical, but again get some pricing info. PPs also had great suggestions regarding a brunch reception mid-afternoon, or late evening, when guests wouldn't expect a full meal. It takes a significant amount of apps to equal a full meal.
I was going to suggest a pasta- easy to go vegetarian with that, and *most* people like pasta. I was also going to suggest stuffed mushrooms. Other options include veggie lasagna, risotto, soup, salad, stir fry and stuffed peppers.
I eat meat with almost every meal. I would never side-eye someone for serving me something vegetarian, but it probably wouldn't be my first choice either. With that said, I think your menu choices sound awesome. You especially have me "sold" on the stuffed portabella mushroom, lol.