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.

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Romero stated that Coinbase will provide customers with access to coins on both blockchains, although they may restrict access following the fork until both blockchains are stable and secure. “We are currently working on the engineering and security requirements for each bitcoin blockchain ,” the post continues.

Although not directly referenced, the post comes just one day after Bitcoin.org threatened to publicly denounce companies that support SegWit2x and do not publicly commit to meet certain demands. In particular, companies must agree to only use the term “Bitcoin” and ticker symbol “BTC” to refer to the original blockchain and may not do anything to “deprive users of their bitcoins”.

The Coinbase announcement appears to meet the second condition since it promises that customers will have “access to bitcoin on both blockchains” following the fork. However, Romero says they will not release a detailed plan for how they will name the two blockchains until closer to to the scheduled date for the fork.

However, the announcement does not appear to have appeased SegWit2x opponents. Cobra-Bitcoin, one of the current domain owners of Bitcoin.org, wrote on Github that the statement “isn’t really helpful” and that Coinbase must “immediately clarify that they will continue to call the current Bitcoin blockchain ‘Bitcoin’ with the ticker symbol ‘BTC’.” This would seem to imply that the announcement is not sufficient to remove Coinbase from the list of companies Bitcoin.org will publicly denounce.

Blockstream CSO Samson Mow — another vociferous critic of SegWit2x — suggested on Twitter that Coinbase’s position may violate the terms of the “BitLicense,” the financial services license bitcoin firms must receive to operate within New York state. Specifically, he pointed to language that prohibits licensees from altering a product or service in such a way that it is rendered “materially different” from its status when the license was approved or raises potential safety concerns and operational concerns.