Which Beatles LP was their turning point?

Into a progressive bent? Was it Rubber Soul? Revolver?

It started with Rubber Soul, and continued to evolve with Revolver.
To be more specific, it was the song, Tomorrow Never Knows (from Revolver), that was a comlete departure from their former songs.

Oops, Meant Yesterday and Today and Rubber Soul! Report It

whichever one Yoko Ono was around to botch

Revolver & Rubber Soul

Revolver was when they started to lose their edge.

Between Help! and Rubber Soul...Some of the songs on help sound like they could be on Rubber Soul...Like Ive Just Seen A Face, Hide Your Love Away, Tell Me What You See. I think it was during the recording of Help! Grass starting influencing them alot

I say it's "Sgt. Pepper's Lonely Hearts Club Band". That album had come out after the group was finished with touring and the results show. They had become more interested in studio techniques by then and now had a bunch of songs they could not duplicate on stage. Before that, nearly all their songs could be performed live.

Rubber Soul had the psychedelia cover, but the subsequent album, "Yesterday...and Today" was the album that made the transition from the cute moppy-haired English lads singing Fifties Rock and Roll style, to the true drug-driven, culturally-influencing music.

This was the album's line-up:

Yesterday鈥?and Today (#1 for 5 weeks, plus another 2 weeks at #2; 31 weeks on chart) (7/16/1966)
Label: Capitol T 2553 (Mono)/ST 2553 (Stereo)
Released: 1966-06-20

"Drive My Car"
"I'm Only Sleeping"
"Nowhere Man"
"Dr. Robert"
"Yesterday"
"Act Naturally"
"And Your Bird Can Sing"
"If I Needed Someone"
"We Can Work It Out"
"What Goes On"
"Day Tripper"

"Revolver" was released after this one.

Rubber Soul

Very interesting question - yup well, it was a progression from Rubber soul to Revolver to Sgt Peppers. Maybe Revolver but Sergeant Pepper was ground breaking stuff ad truly a big step forward in the world of Rock. Fantastic album that should stand at the top of the tree (in my view). I heard it when it first came out and it blew me away . The finest work that George Martin ever did!
ps Rubber soul does NOT have a psychedelic cover - that is Revolver! (see answer above)

Rubber Soul is where you really notice a difference. Thank goodness they stopped that 'love me do' stuff.