The correct sentence that follows punctuation conventions is:
"Many customers have asked, “Does milk from grass-fed cows taste better?”"
The other sentences contain punctuation errors or missing commas. Here are the issues with them:
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"However the ice cream has very few ingredients." - Should have a comma after "However": "However, the ice cream has very few ingredients."
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"The state’s most popular ice cream shop is in Boulder Colorado." - Should have a comma after "Boulder": "The state’s most popular ice cream shop is in Boulder, Colorado."
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"Although the creamery uses dairy from many producers; it sources it’s eggs from one farm." - The semicolon is incorrect here and should be a comma: "Although the creamery uses dairy from many producers, it sources its eggs from one farm." (Also, "it’s" should be "its.")