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Some share Ms. Roup’s belief that it aids digestion, lessening bloat and constipation; others point to its benefits for skin health, believing it wards off the formation of wrinkles and clears up acne.

Ms. Roup is one of many influential figures who swear by the drink, which counts Gwyneth Paltrow, Jennifer Aniston and Gisele Bündchen as devotees.

For now, Ms. Roup, who is quick to tell her followers that she’s not a nutritionist when sharing her dietary habits, has more faith in this route than other options on the market that make outsize claims.

Every morning around 7 a.m., as she prepares to film a live workout for her 237,000 Instagram followers from her New York City apartment, Megan Roup sips on warm water with a squeeze of lemon while her French press coffee brews.

“It just get things moving and grooving in the morning,” said Ms. Roup, a fitness instructor in her 30s who founded the Sculpt Society workout beloved by many models.