What is the purpose for your social media involvement?
Before jumping on social media, it is helpful to ask why you might consider doing so and working toward agreement as a couple. This agreement will help you decide what platform you use, whether or not your page is private or open to the public, and whether or not you allow comments if the platform allows you the option of turning them off.
If the purpose is to rant on social and political issues, blow people up, troll others, harass, and act like a digital arsonist then one has to ask if this is the best use of their life energy. Perhaps finding pretty much anything else to do other than social media would be a better choice.
Is the purpose largely marketing to expand a business? If so, then the page should be very professional and public.
Is the purpose largely ministry to share Bible verses and other encouraging resources to help people? If so, then the page should be somewhere between professional and personal and be more pastoral and public.
Is the purpose to keep family and friends up to date on how life is going and share family updates? If so, then the page should likely be personal and private so that trusted people can communicate in a safer context.
Do not, however, fool yourself regarding privacy. As soon as something is posted on social media there is always the possibility, even inadvertently, that what you share spreads beyond the intended audience.
When a couple does not agree on the overarching purpose of social media then there are battles that rage over specific posts and pictures. Hopefully, agreeing on what the point of social media involvement is and is not can reduce the battles between the couple with a battle plan for the couple.