How to deal with people you aren't planning to invite requesting an invite

Well first it’s incredibly rude to ask someone for an invite to their wedding so you are not the ones being rude in this situation. If someone asks you for an invite, I would say something along the lines of

“Due to the venue capacity we are limited in how many guests we can invite.”

I always tell people that we are having an intimate ceremony. We are still inviting 100 so by no means is a small wedding, but by "intimate" I mean people that I regularly talk to or that I'm close to. It's rude for people to assume they are invited to a wedding, but don't let anyone know ahead of time who hasn't asked about it yet. Only address the people who question you or him about it.

It's rude for people to assume they are invited or even ask! So you're not rude if you're responding to a bad question!
I'd say "Were sorry but the venue has a strict capacity on attendees and we are full"
Or if it's someone you don't speak to often "We are hoping to have a more private and intimate ceremony"

“We wish we could invite everyone, but we unfortunately have budget and space constraints so we have to limit our guest list.”

I'm a "keeping it casual" kind of person. I'd just tell them simply "We have really big families, so our venue is at capacity."

If you plan to invite 230 and your venue cap is 180... you are in trouble. You are going to be over. I wouldn't invite more than 200 and even that would give me anxiety. What's going to happen if more than 180 RSVP? It's more rude to cut people at that point and explain that you over-invited and there's actually no room for them. Contact your venue and tell them you are sending 230 invites... they will quickly tell you it's a BAD IDEA... which you can show your fiancee. I think people overestimate RSVP declines.

I've had to deal with that too! I just told them that we're dealing with family first and due to our budget we can't invite a whole lot of people. I had a girl I served with in the military claim that she should be invited because we're best friends but 1. we don't really talk much AND 2. she was like the only one that was against my relationship from the start because of our age difference. Granted, we were closer overseas working together but kinda drifted after that so it's like what are you even talking about?

Just say "I'm sorry, we would love to be able to invite everybody, however our venue has a limit and we cannot go over that."