Call it a brew-haha over whether this upscale coffee joint is a restaurant, or an eating and drinking establishment.

Either way, residents of a luxury building in a trendy part of Manhattan don’t want it anywhere near their pricey homes.

A dispute about that fine distinction is percolating at Ralph’s Coffee in Flatiron, which is planning to move to 140 Fifth Ave. at 19th Street from its current location just two blocks north.

Ralph’s — the coffee arm of brand behemoth Ralph Lauren — is on the verge of signing the lease. But the lease prohibits a restaurant, and the residents living in the lofts above, which sell for millions of dollars, are suing to keep Ralph’s out.

They are concerned about noise, trash and vermin, which plagued them in years past when a rowdy Russian restaurant occ

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