At least twenty years ago, from scripture I came to the following as a definition of worship. It is my definition, but I believe it reflects what the Bible says. "Worship is acknowledging or recognizing God for Who He is according to His Word and giving Him what He says that He wants." If I were going to add a secondary important aspect, "worship necessitates coming to the right God and in the right way." You aren't worshiping God if He isn't actually God and then you're not worshiping Him if you are doing it your way. God doesn't accept just anything.
I googled the two terms "worldly worship" and it produced 12,300 results. Those were not all articles written by me, although I found I had used that terminology in some online writings. It is a known concept though, worship that is worldly that is not acceptable to God, which is of the nature of the world system and not the nature of God. I went ahead and googled "syncretistic worship" too, because I think it's a related concept. That showed up 6,060 times.
Syncretize means: to "attempt to amalgamate or reconcile (differing things, especially religious beliefs, cultural elements, or schools of thought)." When referring to syncretism in worship, many have pointed to the practice in Israel of bringing aspects of the worship of paganism into the worship of God, mixing the two. Many examples of syncretism are seen in the nation Israel (Exodus 32:1-8; Leviticus 10:1-7; Deuteronomy 12:30-31; 1 Kings 3:5-10; etc.). The way Israel syncretized is not the only way to syncretize. Mixing something impure with purity makes it impure.
Speaking of worship, Paul commands, "be not conformed to this world" (Romans 12:2). Because God accepts only holy worship, not profane, then it can't be conformed to this world system, the spirit of the age. Obviously, everything we do occurs in this world or on this planet, on earth. The world system clashes with God. It is represented by darkness and all the characteristics described in scripture as seen in many places, one of which as an example is James 3:15: "earthly, sensual, and devilish." There are many more. One should assume that all of these can be understood and applied.
The world is attractive to sinful flesh. Satan shapes the world system to lure people away from God. Because the world is a lure, it also works when a church uses it. Satan designs it as a lure and if a church takes that lure and uses it, it's still a lure. That's the temptation of using anything worldly.
Varied aspects of this world are filled with meaning. Many of those meanings are not congruent with God. One should even expect that they are not. Whatever it is that will please God has already been around. One should question any new style or method, especially that has proceeded from worldly lust, which Titus 2:11-12 says that the grace of God teaches us to deny. I contend that rather than denying worldly lust, most churches today promote it. They might argue that this new way is neutral, neither good or bad. God's people didn't originate it, actually rejected it, and then after a period of time, accepted it, then used it, arguing now that God also wants it.
Someone may ask, what basis do I have that churches are using worldly music? I haven't been in all these churches, so how do I know? Not only have I been all over the country, but I've looked at websites of churches all over. I know enough.
Every church and their leaders should want accountability as to whether they are using worldly worship. They should look for constructive criticism. People are deceived in many different ways as they relate to God. The broad road to destruction has many religious people on it. When I read the materials of the church growth movement used as a model for thousands of churches, they encourage worldly worship as means of church growth.
God doesn't accept worldly worship, so why would churches still do it? Why would Nadab and Abihu offer strange fire to the Lord? I would contend that the strange fire of Nadab and Abihu is a lesser perversion of worship than most worldly worship, and God killed them for offering it. They were still offering incense. They just changed the recipe. They offered something God didn't say that He didn't like. They offered something different than what God said He wanted. It seems that Nadab and Abihu just didn't take God seriously, what could be called, not fearing God. We know what they did was bad and wrong and sinful, but it was still not something that God had said was wrong.
Worldly worship we know God doesn't want. There are two obvious motives for giving God something He doesn't want, and they are seen in scripture. First, the one offering it likes it. This is the serving the creature of Romans 1. He's not really even giving to God as much as he's doing something for himself that he likes. I've seen this again and again in churches I've visited. It can happen anywhere. Second, other people will like it too, so it will make the church more popular. The people wanting that worship don't like what God likes, but they either convince themselves or are just deceived into thinking that God will accept it. A third reason is deceit. The feeling the worldliness causes often is mistaken for a spiritual experience.
Worldly worship parallels with a worldly life. The world offers what the flesh desires. There were times in church history that a wide chasm existed between the worship of the Lord in the churches and the world. That gap has shrunk to where there isn't much difference. It's worse that that. The churches like the world and they expect God to like it too. It shows an amazing lack of understanding of God and what He wants.
As you have read this, reader, perhaps you wanted to know more specifics. "Give me a specific of worldly worship." I could say, using the world's music in worship. To get more specific, I could go further, using rock music in worship. There are many other specific examples. It's better to start with the principles for discerning what is worldly and that God doesn't want something worldly.
To accommodate worldliness, I have heard evangelicals give a very narrow understanding of worldliness as internal only, that nothing external is worldly. However, Paul wrote, "Be not conformed to this world." There is internal worldliness, the love of the world in the heart, but conforming by definition must be external. God doesn't want something we can see and hear is worldly. He rejects it.