If it's such an obstacle for social life, I'd just give in and make an account. Given the alternative is "exchanging phone numbers" (with the intent to text or call, presumably) I'd say Instagram is no worse privacy-wise - both offer absolutely no privacy protection. If a phone number is required to register (I don't know if it is), I'd get a bootleg sim specifically for it. I would treat all communications on any proprietary platform (even 1-on-1) as though they are happening in public (Twitter-style). Avoid using apps if at all possible as they have more access to your device. If that's not possible, at least do not give those apps any permissions, however hard they are trying to eek them out of you. Do not use it for anything but chatting with your acquaintances - merely looking at your feed, even without any explicit interactions like opening a post, gives Meta a lot of data about you.

If the connection moves on from "acquaintance" to "friendship", perhaps try pushing them towards a better platform - I recommend Matrix as it is federated (unlike Signal), and has pretty nice clients/UX nowadays (unlike Tox and XMPP), and is e2e-encrypted (unlike almost everything else).

Find a way to use Instagram to drive them to another app, like this: https://lemmy.world/post/21620691

Anyone have any advice?

• Ask them for their number, and see how it goes? Worst case, they will say 'no', end of the story. Maybe the will ask why you don't have IG and that will be the start of an interesting conversation.
• Try to meet different kind of people? I mean it seriously. I know a lot of people around me who have IG/Facebook/X and so on but at the same time none of them make it a requirement to use it.
• Use a second phone/number for that crap content only? I barely use my 'real' phone (I have nothing installed on it beside what I'm required to use) still I do own a second phone just so I can easily share a number with all the services and various craps that ask for one. It's a phone I never answer to, despite it being constantly harassed by callers. And that peace of mind (my real number is almost spam free) only costs me the 2€/month (plus the phone, I purchased used). You should be able to do something similar for social networks: have a second phone without anything personal on it, just with IG.
• Accept that you're doomed to use IG because it's with those 'IG people' and no others you want to spend your time with? I like to spend time with people reading books, it's kinda expected we indeed read books. Would I not like to read, I would not spend as much time with them.

I've gone back to just texting and switched over to signal for band chats and group stuff, and so far the only person who doesn't like it is a dick bag who claims to be an anarchist but refuses to live his life without using a fascist propaganda machine to socialize.

What about email? Just create a new one just for this stuff. Go back to giving out just an email. Everyone has one of those too and it's not as 'archaic' as a phone#

Gonna be real with you, if you're in the US and wanna connect with pretty ladies you pretty much have to have insta or messenger. If they are devout apple heads they might wanna do iMessage but as I don't use apple products I can't speak to that. I personally don't want anyone to have my phone number. I have signal, messenger, whatsapp, Kik, WeChat, and discord because I travel a lot and I have contacts on all of them. People prefer social media so they can remember you, your interests, things you say publicly, and use that to help decide if they wanna hang.

Are you meeting people 15 years ago?? We've known everything mark zuckerberg touches is trying to kill you for money for a long time.