Bill,
If you believe that is the truest description of all false religion, then is that how you describe your witnessing targets when talking to them? "Hey, you know you're worshipping Satan, right?" I'm going to guess you don't. Safe bet.
OK, so this description we were given in Rev. 2&3: was that intended by the Holy Spirit to be the most essential and accurate description of every false religion? Of all Jewish synagogue worship? Or was it a particular epithet? I think so.
Is all false religion ultimately connected with the father of lies? I'll grant it. I think idolaters end up serving demons, even though they seldom aim at such service. But there is a great variety in the level of direct/indirect demonic influence.
I think it's hard to make a good case that some relatively meek or peacenik Jews, Torah observant and quite serious about trying to be personally holy and against sin as the Law defined it, who are not inclined to persecuting the church, are "satanic assemblies" by a biblical definition that all of us (in this discussion) can agree upon.
Our Confession speaks of some churches that have so degenerated the best description of them is: they've become "synagogues of Satan." That's a borrowing of the description from its original setting. It was particularly applicable to the irreformable, corrupt, and murderous (Jn.8:44; cf. 1Jn.3:12) Roman communion, which sought the literal destruction of gospel churches.
We should decide, with judicious care, which religious companies deserve such a name; and which are just wrong, which are (thankfully) not as bad as they could be, which are pathetic, and which are ridiculous. We should be glad Satan doesn't have the kind of limitless power that would let him free to make every false way an unholy temple, and every unbeliever a Gadarene demoniac.