I've heard many times that salvation is a "free gift" and one can do nothing to earn it, and that's what sets Christianity apart from other religions. But obedience to Jesus is another important part of salvation. So how can we truly say one doesn't earn salvation when they must be obedient to get it?
This is an important question. Since the 1500s Protestant Christian groups have defined grace as "unmerited favor" and salvation as a "free gift." To illustrate, some translations of Rom 6:23 change gift to free gift. Yet the word "free" is nowhere in the Greek.
I agree that companies offering things "free," when actually there is a hitch -- like a purchase being required -- are being sneaky. Yet the catch doesn't necessarily mean the gift isn't a gift. By definition, a gift is something given. What is wrong isn't the condition necessary for receipt of the gift, but the decision to conceal this and pretend there are no requirements.
Jesus makes it crystal clear that salvation requires obedience. Faith without obedience is dead, as his half-brother James put it (James 2:26). Works are necessary for salvation (James 2:24). At the last day, many who think they have done the right things will be in for a shock (Matt 7:21-23), as will those who have failed to live out their faith (Matt 25:14-30). Since obedience is required for salvation (Acts 5:32; Heb 5:9; Rom 1:5; etc), the Lord was very upfront about the cost of discipleship (Luke 14:25-34; 9:57-62).
Now I myself have frequently made the point about which you are asking. In Christianity, God reaches down to man; in human religions, men by works try to reach up to God. I admit this may be an over-simplification, but it is not far off the mark. That's because Christianity isn't a system of religious works, or even a religion at all (in the standard sense), but a person. For us "the way" (see Acts 9:2; 19:23; 24:22) isn't a system, but a person (John 14:6: "I am the way."). The basis of our faith is a relationship with a God who is seeking us, more than in our own religious cleverness or personal sacrifices or human intellect.
Protestantism overreacted to Catholicism, with its many works -- not works of Christ, such as caring for the poor, spreading the word, or living a holy life, but man-made requirements like rote prayers, pilgrimages, relics, and so forth. Martin Luther added words to the Bible; instead of justification by faith, Luther added the word alone, for example in his translation of Romans 3:28. (So halten wir nun dafür, daß der Mensch gerecht werde ohne des Gesetzes Werke, allein durch den Glauben.) He also erred in interpreting works of the law as any righteous deeds, whereas in Romans and Galatians, Paul is speaking of works of the Law of Moses (principally circumcision, Sabbath, and keeping kosher).
So what about Eph 2:8-10? Are we saying that we are saved by doing works -- a do-it-yourself religion? Not at all. We can't "work" our way to God. Salvation is a gift; it is "not of ourselves." Still, we must invite Jesus to be our Lord before we are saved (Acts 2:36-40) and continue to live in service to him as Lord (Col 2:6; Matt 7:21-27).
There's even more evidence that the Protestant view isn’t quite right. Luther rejected James (he could not agree with 2:24), claiming that it was an "epistle of straw." Nor did he accept Hebrews ("There is nothing of the gospel" in this letter). Many times Hebrews states that we must maintain our salvation, or we can lose it. There are easily a dozen verses in Hebrews making this point. Rather than me listing them all, why don't you have a quick read through Hebrews and find them yourself? -- the exercise might be good for your conviction. At any rate, Luther removed four books from the N.T., reluctantly translating them and then placing them in an appendix to the 23 N.T. books he considered to be of God.
There are two points the Protestants are missing.
  • First, salvation comes in two stages. Past sins are forgiven in baptism, yet full salvation is still future (2 Tim 4:18; 1 Cor 9:27; Rom 2:7-10). If we deny Him, he will deny us (2 Tim 2:11-13).  Like the man who cancelled the huge debt in the parable — it is possible for the debt to become “uncanceled” (Matt 18:32-35).
  • Next, grace is not "unmerited favor," if this means that we need not respond to God's truth before receiving his grace. The Greek charis is an extremely common word in the N.T., as well as in the Greek O.T. -- although interestingly Jesus uses it only 4 times, and it doesn't appear anywhere in Matthew or Mark. Favor (grace) is extended typically when one has done something well. "Well done, good and faithful servant..." (Matt 25:21). To claim that grace was not shown to the servant on account of the servant's obedience is nonsense. Rather than construing grace as unmerited and without conditions, we ought to realize that God's favor is conditional. The failure to understand grace explains well the lack of discipleship in virtually all Protestant groups, and all the more in those groups who claim it isn't necessary to do anything to be saved.

There you have it. I may have written more than you expected, but it's such an important question -- and one I have pondered a lot this year [2016] -- that I wanted to share my thinking with you. God is no less gracious because his continued forgiveness depends on our obedience; salvation can be "canceled" (Matt 18:32,34). And salvation comes in two phases. Pretending that the first phase alone brings unconditional forgiveness is dishonest. Of course it would also be biblically wrong to claim that the second phase "earns" salvation. We can't earn it, but we can appropriate it -- by doing what pleases the Lord.