“For all who have sinned without the law will also perish without the law, and all who have sinned under the law will be judged by the law. For it is not the hearers of the law who are righteous before God, but the doers of the law who will be justified. For when Gentiles, who do not have the law, by nature do what the law requires, they are a law to themselves, even though they do not have the law. They show that the work of the law is written on their hearts, while their conscience also bears witness, and their conflicting thoughts accuse or even excuse them on that day when, according to my gospel, God judges the secrets of men by Christ Jesus.” (Romans 2:12-16)
According to this passage God is no respecter of persons and will judge all people (Jews and Gentiles) equally, whether they had the law or not. The whole point of this passage is that a person was held accountable in the Old Covenant times by the natural law inherent in nature and testified to by the human conscience—before the revelation of Christ was revealed. Both natural law and the Law of Moses serve only as schoolmasters leading us to the Savior because knowledge of sin should lead us to cry out to God for His mercy and salvation by grace.
(Galatians 4:24 and Romans 2:12-16 go hand in hand. Both show that Jews who had the law and non-Jews without the law have no excuse before God—the former passage because of divine revelation through the prophets, and the latter passage because of the revelation of God through nature and natural law. See also Romans 1:18-22.)
Some good people I know and respect do stretch this passage to lay open the possibility that those who have never heard the gospel will have a chance to be saved if they follow their conscience and attempt to seek God with all their heart, even if they never know the full revelation of God in Christ. Of course, I don’t think this is what Paul is saying here in the context of Romans, and I would not want to take a chance and give people a false hope based on an ambiguous understanding of this passage.
Also, the Bible tells us that even those who have never heard the gospel are without excuse and will be held accountable because of the wonders and beauty in creation which declare the glory of God (Psalm 19:1-4). God promises all, whether they have heard of Christ or not, that if they seek Him with all their heart they will find Him (Jeremiah 29:13).
Finally, the entire Old Testament, especially the writings of the prophets, shows us how God feels about sharing His glory with other gods and/or religious beliefs (Isaiah 42:8). Here is a passage from 2 Kings 17:35-41:
