The Resistance, a US-based Christian group, has called for a national boycott of the coffee-selling giant.
It says the chain's new logo has a naked woman on it with her legs "spread like a prostitute... The company might as well call themselves Slutbucks".
Starbucks says the image - based on a 16th century Norse design of a mermaid with two-tails - is not inappropriate.
Rather, the image is a more conservative version of the original Starbucks design, which hung above the chain's first store when it opened in Seattle's Pike Place Market in 1971.