People here keep talking about the direct influence the Beatles had on specific musicians but forget to take in the indirect butterflies that would take place as well, this why that Yesterday movie sucked.
With no British Invasion the lives of a lot of British musicians is changed big time, for example the Yardbirds might not get a recording contract, they then don't record the single "A Heart full of Soul" Eric Clapton doesn't quit the band in protest and he and the rest of the band may not ever be heard of by anyone outside of London.
Jimmy Page may never get studio work and might not ever meet John Paul Jones or Robert Plant and John Bonham.
Ozzy Osborne never asks his dad to buy him a P.A. system and Terry (Geezer) Butler never trades in a train ticket to a monastery to become a Lay Brother and instead goes and buys his first bass guitar after a friend loaned him his copy of Sgt. Peppers.
A lot of other butterflies could cause huge changes in the lives of not just musicians but people who became agents for rock bands, studio technicians and other careers which may not be music related but still had an effect on people who were in the music business.
Also the Beatles influence on musicians does not end in 66, bands like Pink Floyd and Queen were heavily influenced by the Beatles later work and there's all the studio technicians and record producers who were influenced by George Martin, Geoff Emerick and their work with the Beatles.
I do think bands like the Doors might not be affected by no British Invasion so psychedelic music might still be big and the Doors themselves might be bigger but they also could be butterflied by ways I can't imagine.
I think Punk rock might still happen especially after a decade of mostly folk-rock music and Punk might be this alternate timeline's British Invasion.
I don't think Zeppelin were influence by The beatles. I also think that The yardbirds would had gotten a record deal if The beatles never existed. I mentioned that British rock groups would had found success in the UK but not really in the US. I think that by the late 60s, a few British rock bands can have a few successes in the US. Nothing like the beatles of course but could they have a few top 40 hits? Its possible.
I mention that Cream could have a top ten hit in america around 1968 without the beatles but could they be superstars? Most likely not.