DUBAI, United Arab Emirates (AP) — Cafes across several Gulf Arab states started selling coffee and other cold drinks in baby bottles this month, kicking off a new trend that has elicited excitement, confusion — and backlash.

The fad began at Einstein Cafe, a slick dessert chain with branches across the region, from Dubai to Kuwait to Bahrain. Instead of ordinary paper cups, the cafe, inspired by pictures of trendy-looking bottles shared on social media, decided to serve its thick milky drinks in plastic baby bottles.

Although the franchise was no newcomer to baby-themed products — a milkshake...