Conditionally include a field (_id or other) in mongodb project aggregation?

There isn't a way currently to do this within the $project stage, but you can use the $redact stage to remove the field conditionally (i.e. you set the value to 0 like you are doing in your example.

db.collection.aggregate(
  ... matching and stuff ...
  {$project: { _id: { $ifNull: [ "$user_id", 0 ] } }},
  {$redact: {
  {$cond: {
    if: { $eq: [ "$user_id", 0 ] },
    then: '$$PRUNE',
    else: '$$DESCEND'
  }}
}