There is no doubt that some of the practices of ancient Hebrew worship bear remarkable resemblance to the worship practices of the pagan nations around them. Other nations practiced similar sacrificial systems, had temples and priests, and many scholars note the the idea of covenants established by God with his people is virtually identical to that of other peoples of the ancient near east.
How can we account for these similarities?
There are at least three possible ways to explain similarities between Hebrew worship and pagan worship. First, some argue that Israel simply borrowed ideas from their neighbors and adapted them. This idea is usually espoused by those who discount the possibility of direct revelation from God, however. In fact, the biblical accounts tell us that every time Israel did that sort of thing, it always led them away from the worship of Yahweh.
The second possibility, one that accounts for the fact that the people’s worship came by way of divine revelation, says that when God instituted worship forms for Israel, he “contextualized” worship in cultural forms and practices they would understand. Andrew Hill argues this for example, saying that the institution of sacrifices “demonstrates God’s willingness to accommodate his revelation to cultural conventions. Human sacrifice was practiced in ancient Mesopotamia, and Abraham was no doubt familiar with the ritual since he came from Ur of the Chaldees (Gen. 11:21).” However, God clearly says that Israel’s worship is patterned after the worship of heaven (Exodus 25:8-9), not after the worship of the other nations.
A final possibility, and one that I believe to be the best, says that the similarities exist because the basic elements of worship existed since the beginning of human history (see this essay). For example, the practice of sacrificing and the idea of covenant can be traced as far back as the Fall, indicating that these kinds of ideas would have been passed down to future generations and would have been in the consciousness of all people from the beginning. The pagans were borrowing ideas from true worship, not the other way around. With the Law, God was simply codifying the structure that had been in place since Adam sinned and that was patterned after the worship that takes place in heaven itself.
Similarities do exist, but the differences are far greater. For one thing, every other nation we know of at the time was polytheistic, while Israel was uniquely monotheistic. For pagans, worship was meant to appease angry, selfish gods; for Israel, worship was a response of gratitude for acts initiated by a kind God himself. For the pagans, immoral acts such as murder and fornication were part of the worship acts; such was not true for the Hebrews.
The central difference between Hebrew and pagan worship is that Hebrew worship is a response to God’s gracious works, while pagan worship is an attempt to appease spiteful gods. Yahweh initiates Hebrew worship. The pagans initiate pagan worship.
No, Hebrew worship, or Christian worship for that matter, is not merely an attempt to worship the true God using forms familiar from the worship of unbelievers.
Hebrew (and Christian) worship is a God-initiated privilege whereby God himself provides a way for communion with him, and his people respond with hearts of thanks and praise.
For a much more thorough treatment of this subject, see my article in the Answers in Genesis Research Journal.