I would prefer my character having as much of a blank slate background and personality as possible, so no I don't think the protagonist should have a family ingame.
I really don't agree on this, Bioware does this WAY too much. Frankly that sounds utterly boring like one of Biowares most recent MCs The Inquisitor.
Molding the character the way you want is fine but having that character utterly devoid of anything in an already active and living world is just...boring. This is why Shepard and Hawke are my favorite Bioware MCs because they can have these things. Shepard can have a family to talk about when speaking with Ashley who is also from a military family and those moment in ME1 & 3 when they talk about or to Mama Shepard is a nice touch. Hawkes run-ins with Carver/Bethany can be happy,aggressive, or sad depending on how you treated them in Act 1.
I say yes to letting the MC in Andromeda having a family. Doesn't have to be Wife/Husband & Kid, could be a sibling or parent. Some connection to the world is always nice, makes it more alive.