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If one is doing work in a kitchen, is one required to upgrade all existing receptacles near the sink to GFCI protection, or can they be left as-is if they were not part of what the customer wanted done?


One is not required to upgrade an existing installation if it passed code in the past, unless it is added to in the present. Then it is considered a new installation, because theoretically it becomes part of the Permit.
Check out BC Safety Authority website for the Electrical Regulations... on Contractors, FSRs, Permits etc.

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a) You must install a 2 pole 15a GFCI breaker to protect that 14/3 circuit, the customer won't like the cost but oh well
Sure, that is to code, but an unnecessary cost to the customer. Personally I would feel bad about not giving the customer their choices. And that is an expensive breaker!
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b) Cap off the black of the 14/3 and hook the red up to a 15A GFCI receptacle, its not code but at least there's GFCI protection if the toaster ends up in the sink, disregard box fill issues
Not code, not legal, but it works. I wouldn't do it... so long as there is 'someone to catch me'.
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c) Open the wall up and fish a 12/2 in there, even though that wall was not originally to have any electrical work done to it. Incur extra cost for patching.
And wire, and breaker, and receptacle, and labour. Say... $2.50/m + $20 + $25 + 2hr labour.
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d) Leave it the way it is, it passed inspection (theoretically) when it was originally installed, perhaps put a new decora outlet on it but don't spend any more time than that. Any new outlets near the sink get put on a 12/2 & GFCI however.
sounds good.