I'd like to add a few comments to Geremia's excellent answer. I was an organist myself, but the church that my family attends now uses contemporary worship and unfortunately classical music isn't that appreciated in that church, which is a great pity. But the worship team on stage really LEADS the congregation to WORSHIP through visible emotion, prayers, and unscripted words (this is not a liturgical church), so those in the congregation that are willing to let their hearts touched will JOIN the worship team in singing, sometimes with hands, clapping, and other physical expression. I believe the organist (plus the choir & music director) has exactly the same responsibility in a liturgical church.
In my opinion, classical style worship has an added dimension that is missing from contemporary worship, which is the ART element, that is, intrinsic beauty in the music itself, while contemporary worship is more PRAGMATIC and in my opinion doesn't have much intrinsic beauty. However, in BOTH styles, the words explicitly direct human hearts to evoke the greatness of God, the love of God (and Jesus), and other expression of faith extolling the works of the Triune God. The words, then, function just like poetry set to music. If the words are written AS poetry (like in most older hymns), then you also have another dimension of ART, but at least when the words explicitly praise God, even simple non-poetic lyrics can do the job.
My point is that when your congregation APPRECIATES the Art dimension in music and/or in the words, then you can potentially double or triple the amount of devotion that your organ performance (and your music selection) can generate in your congregation. As an organist we are servants to the congregation. So in a church setting the measure is more in terms of how well the congregation's DEVOTION toward God increases, while in a concert hall setting the measure is how well the music critic (or the paying members of the audience) is satisfied.
So in my opinion that's the sticking point. People are simply different. Some who are not artistically inclined can worship God better with contemporary music, but some like myself can worship God better with J.S. Bach St. Matthew Passion or Mass in B Minor for example. I really have to humble myself not to feel superior to them, so I mostly pity them for not taking the advantage of praising God with more dimensions, because I believe that some attributes of God that are True, Good, and Beautiful ARE communicable to a human heart (sadly this is no longer majority opinion).
So to answer your question about stops, polyphony, embellishment in hymn playing, or I can add chorale preludes, if I WERE your congregation, I WOULD LOVE IT, and yes, I would evaluate your performance artistically, but as a believer I have to remind myself that this is church, not concert hall, although I WILL thank you after service for preparing well if you perform J.S. Bach's chorale prelude sensitively and artistically, for example. But if the congregation is not that appreciative, as a worship servant to lead congregation MORE to God, you'll have to adjust your music selection accordingly.
Notice one important difference between classical performer and contemporary worship leader, both tasked with leading the congregation to worship God. As a member of the congregation I would NOT try to get clues from your emotional state while playing the organ as opposed to being led visibly by a contemporary worship leader to increase my devotion to God during worship. VERY DIFFERENT. Contemporary leader is like rock star on stage, whose function is to sympathetically induce similar devotion within the congregation. BUT we as classical organists's job is to produce the artistic SOUND which is the agent that stirs the congregation's heart. It's lot more impersonal, but both the VISIBLE sign from contemporary worship leader and the AUDIBLE sign from the organist serve the SAME function, that is, to stir the congregation's heart to worship God. The congregation also has the SAME responsibility: to let themselves be touched. I can be aloof in a contemporary style worship (because I don't like the music), but I would be failing my responsibility to God (why would I come to church, then?). Similarly I can easily imagine a member of the congregation who doesn't like J.S. Bach refuses to let his heart be stirred by the triple effect beauty of Mass in B Minor so he can be more devoted to God.
Moving on to how God looks at your own service as an organist. I'm aware that you are not a believer, but regardless, if you do your job well as I described above, then maybe one day when you become a believer Jesus will say to you: "Well done, my good and faithful servant. You have been faithful in handling this small amount, so now I will give you many more responsibilities. Let’s celebrate together!" (Matt 25:23-25).
If you are a believer like myself, then even the act of preparation can be worship itself, because while practicing you can worship God in your heart. What Father wouldn't be pleased to see his children give their best to Him? People think that's why God appreciates Abel's sacrifice, not Cain's. Sometimes when I'm in certain mood, it's hard to hold back tears during my own performance because it can affect my playing. Similarly, sometimes I see a contemporary worship leader got so carried away with what the words that are being sung that she has to hold back emotion when leading the worship (who can sing well when you're sobbing?)