Jacob Elordi's letting his cares melt away under the warm Italian sun ... flaunting his six-pack alongside girlfriend Olivia Jade Giannulli -- all while some back in the U.S.A. are blasting his recent casting in "Wuthering Heights."

The actor and his GF his the Italian coast with her family ... and, clearly he enjoyed the refreshing blue water in the Mediterranean -- launching himself off the boat and into the surf repeatedly.

He's dripping wet in most of these pics ... flaunting his six-pack in just a pair of navy blue shorts while his better half seemed to mainly stick to the shore and the ship.

She's tanning in a lavender-colored two-piece bikini ... brushing her hair and stretching out beside her man on the deck.

Not a ton of outright PDA here -- after all, OJG fam's on the ship with them -- but, there are a lot of flirty moments between the two on the vacation.

The two look unbothered on their European excursion ... so, it seems the controversy surrounding Elordi's upcoming turn as Heathcliff from the classic romance novel "Wuthering Heights" isn't getting to him.

ICYMI ... Elordi has been cast alongside Margot Robbie for the film adaptation of the book -- preparing for a UK shoot in 2025. The casting got people up in arms 'cause the book describes Heathcliff as a "dark-skinned gipsy" who was abandoned as a baby in Liverpool, a well-known slave port back when the novel was written.

So, people have always kinda assumed Heathcliff was Black -- which JE obviously isn't. Worth noting, the book's author Emily Brontë never comes out and says it specifically ... but, still, some people ain't happy about the casting.