Is it true that the F-4 was harder to target with heat-seeking missiles due to the shape of the empennage? If so, then why don't modern aircraft use a similar design?
I have no comment on the ability of the tail design making the aircraft more difficult to target with heat seeking missiles but I can give a few educated guesses on why this tail design is not often repeated.
The steep downward droop of the stabilizer implies it is producing a downward force to hold the nose up rather than contributing to the lift. Wings on airplanes have this V shape so that the vector of the force the wings produce is upward and inward. Should the plane roll then the wing that drops has more vertical force than the opposite wing, these forces are equal only with the plane level. This keeps the plane on a level flight naturally. An inverted V tail can achieve this same self leveling only if the forces it produces are now pointed down. If the stabilizers were contributing lift then a roll of the plane would produce more lift on the wing that was raised in the roll, this then produces more lift and a positive feedback on the roll making the aircraft inherently unstable.
Using stabilizers that produce a downward force instead of lift is inefficient. It is producing drag on the craft with this force and not contributing to the lift, meaning the wings need to counteract this downward force with more lift, and this lifting force not only must lift the craft but counteract the downward force of the tail.
This was likely an engineering compromise as there is no inherent reason that the tail cannot also contribute lift. There was no doubt a center of gravity problem on the wing placement and it was easier to have this less efficient tail than to redesign the entire airplane.
So, one reason this is not repeated often is because it is an inefficient tail configuration. Another reason for not having an inverted V tail design is that with modern computers it is possible to achieve stable flight without any canting of the wings and control surfaces, this brings higher performing aircraft.
In high performance aircraft like fighter jets the engineers will want to remove drag where they can. The canting of wings to get an inherently stable configuration means that there is an always present inherent drag. On aircraft that carries passengers this inherent safety is an acceptable compromise as it gives a failsafe for a computer failure. On a fighter jet this failsafe is removed because the gain in performance is vital. There will be redundant computers to provide some level of a failsafe against flight control computer loss, just not in the wing and control surface configuration.
This is an inefficient design made no longer necessary with modern flight control computers. I've seen this kind of tail on military drones before. This also appears to be an engineering compromise in getting an existing drone design to carry heavy observation equipment in it's nose without having to redesign the entire craft or make large changes to the flight control computer. With bigger wings, an inverted V tail, and maybe a more powerful engine, they can get something flying with the intended payload quickly.