Morena

Morena is used to refer to a person with dark skin or hair (typically).  It’s not an insult at all, and neither is negra or negrita.
There are plenty of "sweet" songs that use these terms.
"Ella tiene cara linda, piel morena. Canela si tu la viera como menea"
Basically talking about how good this girl looks, and one of the characteristics she has is "piel morena" -dark skin.
"Mi negrita linda que es lo que tengo en mi corazon. Que ya como ni duermo sigo pensando solo en tu amor"
Talking about he loves his black woman so much he can’t sleep because he's thinking about her love.
And the list goes on.
And La Negra Tiene Tumbao by Celia Cruz is all about this "negra"- about this black girl that’s just so bad that she doesn't have to show off like the other girls do to be considered attractive. It’s all in her essence lol. She’s graceful, and confident, etc.
In English, people often consider it rude to call someone by their physical characteristics. In Spanish, it’s not that way especially if you add -ita/ito to the end of the word, which basically makes it affectionate.
It’s not uncommon for you to hear words like these:
Rubia- blond haired girl
China/chinita- Asian girl
Gorda/gordita- fat girl (which, believe it or not, is used affectionately sometimes)
Flaca/flaquita- skinny girl
Etc.

None of the above are in themselves offensive, it’s about intonation.  Most likely, the guys that say that are just trying to greet you or get your attention, or they're hitting on you.