Interestingly, the OT saints and, I assume, many NT saints, had two burials! The first was either in the ground or in a cave or crypt, if they could afford it, and after the flesh had decomposed and only bones remained, the bones were reburied in an ossuary, or miniature casket of stone, and then "reburied" in the crypt along with other deceased family members, each in his or her own ossuary. Today, of course, it is not uncommon for relatives of the deceased to bury the loved one in a place specified by the person prior to his or her death, which more often than not is in close proximity to the graves of other family members.
I cannot speak to RC tradition regarding this issue. Furthermore, I think the Bible does not weigh in on this question, at least directly. As with so many potentially controversial issues, we need to be guided, rather, by general principles and not specific prescriptions or prohibitions. In other words, in many issues God gives us liberty to do one thing or another, but we must never flaunt our liberty before a brother or sister in the Lord, or within local assembly which may not have the same liberty as we do.
From Romans, chapters 14 and 15, and 1 Corinthians, chapter 9, then, we can glean some helpful guidelines regarding cremation versus burial, and many other issues besides.
We need to be fully convinced in our own minds about a particular liberty we believe we have (Romans 14:15). In other words, we need to look deeply into our motives for believing the way we do. Are we truly convinced of the rightness of our liberty or are our motives mixed with doubt or obstinance or some other dishonoring-to-Christ attitudes. Some Christians, for example, tend to be "contraries" who when another believer says "I believe __ to be right" says, "Well, I believe ______ to be wrong!" Many other base motives can also be at work, but I'll leave them to you to imagine. Furthermore, whatever attitude or action, belief or behavior, does not proceed from faith is sin (Romans 14:23).
We as Christians hold our beliefs within a community of other believers whose beliefs, convictions, liberties, scruples, and sensitivities are going to be different from ours. This isn't a bad thing; it's perhaps simply the normal state of affairs within any given assembly of believers. God doesn't make duplicates, only originals. God also gave us one mouth, but two ears, so that we'd listen more than we speak. In other words, we can almost always learn from a brother or sister who feels differently about __ than we do. "None of us lives to himself, and none of us dies to himself" (Romans 14:7). No man is an island, as John Donne (and Paul Simon, of Simon and Garfunkle fame) said. This does not mean we have to give up, say, having a glass of wine with our meal just because Sally feels strongly that the drinking of wine is "sinful." It does mean if we happen to be dining with Sally we forgo the glass of wine for her conscience's sake. What we do in the privacy of our own home is between us and the Lord. This guideline is not much help regarding cremation versus burial, but it does serve to make us more sensitive to the consciences of others. Sometimes Christians simply need to agree to disagree agreeably, which is more difficult, I suppose, for the person who does not share another brother or sister's freedom. This does not mean that a local assembly cannot have, and state, a policy regarding a controversial issue; it does mean that policies not based on the clear teaching of God's word need to have some wiggle room for differences of opinion and liberty.
God judges us as individuals, and we fall or stand before Him alone. Each of us bears his or her own load (1 Corinthians 10:29; Galatians 6:5). Being judgmental in any given area of freedom is not fitting for Christians within the local church. Overt sin is one thing; a grey issue is quite another.
Biblically, the norm in both the OT and the NT seems to have been burial, but even so, only the rich could afford burial in a cave carved out of rock. Jesus was buried that way, not because He was wealthy, but because He had a disciple who was (Joseph from Arimathea). Joseph and Nicodemus (see John 3) brought burial cloths and 75-100 pounds of spices (myrrh and aloes) with which to "anoint" Jesus' body (John 19:38-42; cf. Isaiah 53:9), which was a Jewish custom in that day.
I italicized the word custom deliberately, because regarding the manner of disposing of the body of the dearly departed, there are bound to be controlling customs in any and every culture, whether in the tenth century BC, the first century AD, or the twenty-first century AD. Customs are not necessarily good, bad, or indifferent; they are simply customs. In the absence of any clear biblical mandate, God expects us to use the guiding principles of the passages I've cited above, as well as a good measure of sanctified common sense.
In conclusion, a godly aunt of mine decided on being cremated rather than buried. Her husband retained the ashes in an urn. Her father, had he been alive when she died, may have objected to her decision, but on balance, he (my very godly grandfather) had surprised me on more than a few occasions with some of his laissez faire attitudes about a variety of things, so I guess I'll never really know whether he would've approved or disapproved. My point is this: the cremation-versus-burial issue may be controversial for some, but as with so many issues, whether we do one thing or another, God looks at the heart. If our hearts are blameless before Him and at the same time His word gives no clear guidance in any given matter, then we are free in Christ to be "pro," "con," or neutral, or even to change from one to the other, as the Spirit leads us.