The fighting isn't between Core and Coinbase, it's between Core and Segwit2x. Bitcoin is going to fork again in mid November into 2 competing chains. If you own Bitcoin on the day of the fork, you will own equal coins on both chains. The bad thing is Segwit2x is not implementing replay protection on their chain. If you own your coin's private keys, you will need to take steps to avoid losing them in replays. You should send your coins to yourself simultaneously on each chain to distinctly different addresses until you have them split. It may take several tries to get it to work. If you leave your coins on Coinbase, they have stated that they will give you coins on both chains and taint them to avoid replays. Someone might disagree with me, but since you're new to Bitcoin, I'd recommend you leave your coins on Coinbase and let them do all the work of getting them on the correct chains. I am going to do it the hard way and split them myself. Once you feel technically proficient at how to do it, I'd recommend keeping your bitcoins only on addresses to which you control the private key as well.

By the way, I hate Segwit2x and will be selling a big chunk of them once I can.