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).