Honestly, I don't think that a band member of the Jimi Hendrix Experience in the 1960s would have actually seen it as disrespectful to cover a Beatles song in their presence (and it doesn't seem to really be discussed in the couple of Hendrix books I have, for better or worse). After all, two years before the release of Sgt Peppers there was a BBC TV special titled The Music of Lennon & McCartney which featured a variety of musicians covering Beatles songs...in their presence. 'Yesterday' was widely enough covered in the 1960s that it sometimes gets claimed that it's one of the most covered songs ever (in the 1965 BBC TV special it has McCartney do half the song, and then Marianne Faithfull does the other half). And not everything in the BBC special was exactly respectful: Peter Sellers' version of A Hard Day's Night is comedic, a parody of Laurence Olivier's portrayal of Richard III in the Shakespeare play. Presumably performed while members of the Beatles were there in the studio (BBC productions like this in the 1960s were basically recorded live), the Beatles almost certainly would have loved it because they had been massive fans of Sellers' comedy group the Goons.

Indeed, Beatles covers were common in the 1960s, where bands felt that a cover of a Lennon and McCartney track not released as a Beatles single might be a possibility for commercial success - that is why you get the Rolling Stones covering 'I Wanna Be Your Man', the Hollies covering 'I'm Looking Through You', Joe Cocker covering 'With A Little Help From My Friends', along with all of the early songs given away by Lennon and McCartney to other Merseybeat/London Invasion bands (e.g., 'From A Window' by Billy J. Kramer and the Dakotas, 'Hello Little Girl' by the Fourmost, 'World Without Love' by Peter and Gordon).

What did change with Sgt. Peppers when it was released on May 26th 1967 was the formation of a rock canon formed around albums, and in which Sgt. Peppers was often to be found at or near the top, with discussion of the worth of the album usually focused on the effort put into the arrangements and production of the sound, and its becoming the first enormously successful rock album that wasn't just a collection of songs but something closer to a symphony crafted together in a deliberate order from individual song material.

Rock being 'canonised' does have an implication of it being possible to commit sacrilege in some way by defacing the music. And some readers will probably have a negative reaction to Big Daddy's comical recasting of 'Sgt Peppers' as 'Poison Ivy' or the Hollyridge Strings' easy listening instrumental version of 'Sgt Peppers'. And so the screenwriter who wrote that dialogue in the 2013 movie is most likely referring to the hallowed halls of the rock canon when he has the actor playing Mitchell or Redding voice concern about disrespect - he's voicing the feelings of 2013 about something that happened in 1967. Sgt Peppers was an instant commercial and critical success: for example, a negative critical comment about it in the New York Village Voice got hundreds of angry letters in reply. But the rock canon did take longer than a week to form, and the change in the way that people saw rock music that happened as a result of Sgt Peppers did not quite happen overnight.

And it's very clear that the Beatles did not feel disrespected hearing their song sung by Jimi Hendrix (who also clearly became a member of the rock canon). Certainly, Paul McCartney - the song's main writer, and one of the people most influential on the production of the album - was clearly very pleased to hear Hendrix's version of the song when Hendrix played it at the Saville Theatre:

I remember him opening at the Saville on a Sunday night, 4th June 1967. Brian Epstein used to rent it when it was usually dark on the Sunday. Jimi opened, the curtains flew back and he came walking forward, playing 'Sgt. Pepper', and it had only been released on the Thursday so that was like the ultimate compliment. It's still obviously a shining memory for me, because I admired him so much anyway, he was so accomplished. To think that that album had meant so much to him as to actually do it by the Sunday night, three days after the release. He must have been so into it, because normally it might take a day for rehearsal and then you might wonder whether you'd put it in, but he just opened with it. It's a pretty major compliment in anyone's book. I put that down as one of the great honours of my career.