There’s no need to detail different denominational interpretations of Colossians 1:15 as there are only two religious schools of thought on this verse. (1) Those who interpret it as meaning Christ has the pre-eminence / priority over all that is created (being their Creator) and, (2) Those who interpret it as meaning Christ was the first thing God created, then God had Jesus create everything else. (A sub-group might be those who say that Jesus only came into created existence at the time Mary gave birth to him, denying his pre-human existence, but that’s just a variation on the same basic theme, so I’m not going to distinguish them here – no offence to such ones!)
(1) is held by all Catholic, Orthodox and Protestant groups who maintain the uncreated, eternal status of Christ, while (2) is held by all who believe Jesus to have been created and who, therefore, must have had a starting point in time.
An overview of the basic arguments of interpretation could be put like this:
In Colossians 1:15 the Greek word Prototokos is used with reference to Jesus Christ. This noun (#4416) refers to a parent's firstborn child. As an extension of this literal meaning, it can also refer to a person who holds a special status as pre-eminent. Those in group (1) hold to that latter meaning – Christ being the first ‘return’ on God’s ‘investment’, as it were, the guarantee of later ‘returns’ in terms of those Jesus saves, while those in group (2) hold to the first, literal meaning.
However, there is another Greek word - Protoktistos - which means 'first created'. Nowhere in the Bible is that word even used, let alone applied to Jesus Christ! Given that the Bible nowhere says Jesus is 'first created', those in group (2) need to explain that fact, but I am not aware of them having done so. There seems to be silence on their part regarding this particular Greek word, but I cannot speak for them. I may be wrong and they have their own explanation. I’m only pointing out an important point that those in group (1) are aware of, and which informs their stance regarding Colossians 1:15.
There is another point that has a significant bearing on what it means for Christ to be said to be ‘first born of all creation’, given that those who say he was the first-created know that that did not imply an actual (literal) birth, for that, in turn, would require a mother to give birth. Fathers do not give birth. So, if those in group (2) say that the Father created Jesus, the Son, as the first created thing, and that Jesus then created everything else, they have to explain why they use the word 'born' when they don't mean 'born'. They mean 'first created'. Yet nowhere in the entire Bible does it say that Jesus was ever created. Those in group (1) encounter no such difficulty due to taking the non-literal meaning of Prototokos, pre-eminent priority as the first ‘return’ on God’s ‘investment’, making him supreme over all that is created.
Now, this is a rather simplistic overview of the two main, opposing, interpretations of Colossians 1:15, but it’s not designed to prove either the stance of group (1) or of group (2). It just flags up some points of difference, to compare one group with the other. But the entire debate hinges on whether the Son is eternal, uncreated, the only-begotten of the Father, or whether the Father caused a Son to start to exist from a certain point in time, who was his first-created one.