I would say he's a young adult, but acts like a kid at heart.

Oh but then again. Many middle aged people (Mr. krab's age) and senior citizens refer to people in their 20s as kids because of the age gap.
Similar to little kids, believing that 17 and 18 year olds are fully mature adults who stand on their own two feet. As we get older, we know that's not always the case and we now refer to 18 -year- olds as kids even though they're of legal age.

He was born in 1986, so now he'd be about 30. He was 13 when the show started, though

I think the one's who call him "kid" are older adults, and to some older adults, he would be.
Look at Three's Company. The main character, Jack, Janet, and Chrissy/Terri/Cindy are all in their 20s or 30s. But Mr. Ferley, and the Ropers - who are in their 50s+, refer to them as "kids."
And a guy I am acquainted with who's in his late 40s, and he feels 20-year-olds are still kids.
Then there' Gloria in All in the Family. She's a grown woman, and married. But Archie, her father, still calls her "Little girl", even though she's not literally a little girl.
Spongebob is a young adult. But he's still very much in touch with his inner child. So he can be very naive and immature.

I don't believe they meant he was literally a "kid", they were moreso calling him "immature" for an adult.

Sponge Bob is 30+ years old. With underwater sponges, in real life, known to live about 200 to 5,000 years, 30+ years old WOULD definitely be considered a "kid"

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They might mean "kid," as in young adult as a early 20 something year old. He is considerably younger than Mr. Krabs and Squidward, and a little younger than Sandy(think Sandy is in her late 20's) He is a few years older than Pearl, who is 16.

I've often wondered this. He seems like one but he lives on his own and works? I guess it's different for Sponges.