A photog caught up with the singer-songwriter outside LAX Thursday, and they talked to her about her choice to shade Diddy ... including forever changing the lyrics to the hit pop classic from "Feeling like P.Diddy" to "F*** P. Diddy," like she did at Coachella last month.

Kesha says she's making the change because she knows what she believes, and she's confident she's in the right here ... and, says she wants fans to scream out the lyrics at her upcoming shows. FWIW, Diddy himself has vehemently denied the allegations against him.

She says she stands by her new lyrics ... adding she couldn't care less about what Diddy and his camp -- who she says haven't reached out -- think about the spicier version.

Kesha also says she's not the type of person to stop talking because people want her to ... and makes a very NSFW suggestion to the industry insiders who don't like the new tune.

Of course, Diddy's dealing with bigger issues than how Kesha feels about him ... facing serious accusations as well as the recent federal raids on his L.A. and Miami mansions.

Kesha's an outspoken advocate for victims of sexual violence ... and, she even once claimed to be a victim of sexual abuse as well.

On a happier note, Kesha says she's performing at a Pride event ... and, she's crediting the gay community for raising pop to the heights it's reached.