First of all, before we give suggestions, we need to know what model of phone you are using/planning to flash an alternative OS to. Not all phones support flashing an alternative OS.
Assuming you have a flashable phone, once you move, you can still have access to your social media app via logging into their web broswer based clients. But to my understanding, not all social media have a web page client - Instagram comes into mind.
Its a lot of hassle compared to the regular way of accessing apps but it is one of the more privacy respecting methods of participating in social media without ever installing its apps.
Do check if your accounts are accessible via your phone’s web browser (or desktop web browser). If they are availble, be prepared to do this in the forseeable lifespan of your mobile phone.
Alternatively, some apps in the F-Droid repository (the “app store” of Lineage OS) has web app front ends like Frost and Slim Social to facilitate access of your accounts. They are still web based but is wrapped around an easy to use app.
All in all, if you understand and accept what you are leaving behind it is worthwhile to switch to an alternative OS.
One more thing. Lineage OS also can suffer from lack of updates. You are, after all, at the mercy of it’s model maintainer. If the maintainer gets bored and gets a new phone or moves on out of the project, you are left without updates on your device. AFAIK, all LOS ports are volunteer run and only goes so far as their volunteerism spirit lives.