Interesting discussion.
I would think that to picket in front of a private home should not be done in any example, as to not punish the children and other family members who are blameless in the actions of their parents/spouses.
A Shul (or even store) may be fair game. A boycott may be more helpful then a picket line.
As an interesting sidenote: There was a store which is known for selling lingerie that opened in a frum neighborhood (due to the large amount of mail order business they were getting from the area). As soon as they opened, a Rov got up and protested against the store, and how these things are very important in private, but can not be shown in public. He ended up leading a protest that closed the store. It just didn’t get the walk-in business they expected, and it wasn’t worth losing good mail-order customers.
Da’as Torah knows when to act, not Da’as Hedyot.