This is an interesting scenario but keep in mind it would be hard to stop the F-15 or a derivative from coming out as the USAF had an institutional dislike of the F-4 as it was a Navy plane but lets take a stab at it, there would have to be some almost ASB political interference to keep them in check and on this path.
the FX (F-15) and LWF (F-16) requirements were formed in the late 1960s as a result of combat in Vietnam.
John Boyd was a major influence in moving the FX towards a lighter and more maneuverable aircraft from early concepts which were heavier swing-wing proposals that were more interceptor than fighter in approach. Say ROE in Vietnam was different, more amenable to BVR combat, and the USAF performed better overall, there is now less impetus to replace the F-4 as it has performed better. The FX program starts and McDonnell Douglas gets picked like OTL but they experience cost overruns and delays that frustrate congress, the LWF program proceeds like normal. Because of overruns and delays congress directs McDonnell and the USAF to study F-4 improvements while continuing with the LWF as a cheaper supplement, from these studies an F-4 with the F-15 wings and avionics is developed and tested along with improved J79 engines (this was a real proposal from McD in 1969, model 98MS/MQ). Despite the USAF's insistence, the FX is cancelled and the improved F-4 is forced on them seeing as the F-4 performed well enough and it would keep some level of commonality across the services.
Incensed with the failure of the FX, the Air Force is determined to get a fighter based on their needs and the LWF happens like OTL, the YF-16 provides impressive performance and higher range than the cancelled F-15 while being cheaper which makes congress happy to go along with it. The Navy is also looking at a light fighter at this time with the NACF program, but congress intervenes again and on the basis of cost and commonality directs the Navy to develop a version of the F-16. General Dynamics teams with Vought to deliver the V1600 powered by an F401 which gains the F-18 designation ITTL. Sparrow capability is ported over to Air Force F-16s earlier than OTL due to Navy requiring it in their "F-18" and this allows older C and D model Phantoms to get replaced with F-16s while the improved "F-4E" fills out the ranks.
With the F-14 as other posters have noted, will come about in some form due to the F-4, even with some proposed variants being unable to reliably carry the AWG-9 and Phoenix. Instead of Grumman, Vought gets chosen to build their V507 due to their track record with the F-8 and A-7 as well as being lower risk compared to the G303 form Grumman. Due to problems experienced with the TF30 in testing, an afterburning TF41 is selected to power the "F-14" and it is introduced in 1972. Later models would introduce the F401 from the F-18 giving a much needed performance boost and fleet commonality.
To keep the Phantom relevant in the 1970s and 80s while the eventual ATF requirements are formulated, a variety of upgrades are undertaken by the Air Force. First the J79 is replaced with the PW1120 providing greater commonality with the F-16 and increasing performance, along with avionics that were developed for the F-15 being put into the Phantom as they are developed. Belly and fuselage CFTs give greater range and allow Phantoms to stop carrying draggy fuel tanks completely. The F-16XL takes the place of the F-15E and allows the F-111 to be gradually taken out of service starting in the 90s with a naval derivative replacing the A-7 in the Navy. Thoughts and criticisms so far?