In the case of a strategic/nuclear war, I imagine there were/are contingency plans to go after the oppositions satellites immediately, and physically where possible, materially take them out.
Yes, U.S. military doctrine includes an ASAT component where advisable, and for scenarios besides nuclear war. The specific technologies vary; there is no magic bullet against a satellite.
Physical destruction requires close-tolerance terminal guidance because of the very high relative velocities involved. As such, whether by kinetic warhead or explosive warhead, accuracy is not assured.
Electronic destruction requires the direction of large amounts of energy toward the spacecraft chassis for a substantial length of time. The pointing constraints and energy density required of the hardware make this highly problematic using even today's technology. Further, the ill-fated SDI programs along those lines soured military strategists into considering this as a first-line ASAT weapon.
The primary defense against ASAT weaponry is inherent: the spacecraft orbital velocity. Predicting where the spacecraft will be at some instant in time
and being able to guide a kinetic or explosive warhead to that exact point in space-time is a demanding problem.
The next line of defense against an ASAT assault is the ability of most military satellites to alter their orbits. If the interceptor can be detected, even approximately, then a well-timed orbital maneuver (e.g., a posigrade boost) can create a sufficient gap in the intercept solution to cause a miss.
The third line of defense is also fairly obvious: redundancy. At any given moment my civilian GPS can see 2-3 times more spacecraft than are required to get a fix. That means an enemy's kiill rate must be very high in order to disable the GPS system. Communication satellites are multiplied similarly to obtain sufficient operational redundancy and downmoding capability.
Even today it is quite likely that a substantial portion of the U.S. satellite fleet would survive a coordinated ASAT attack, although there are presently only two other countries on Earth with the capability to mount such an attack. This is the Liberty-ship principle: build and deploy more targets than your enemy can destroy. That is not met by a small number of monolithic installations but by a large number of modestly-provisioned (i.e., cheap) ones.
Would orbital velocity save an unmanned lunar base? No, the Moon plods along in its orbit at a very predictable, extremely sedate pace. Several nations today (and two during the Cold War) demonstrate the ability to land projectiles with considerable accuracy on the lunar surface using only orbital mechanics. That also refutes the alleged distance defense. Would orbital velocity save a spacecraft at the Lagrange point, even if you could somehow park one there? No, for the same reason. The rendezvous problem in either case employs the same proximity tolerances but vastly broader velocity tolerances. That's why we could land ballistic projectiles in small circles on the Moon decades before we could hit satellites in low Earth orbit.
Would maneuverability save an unmanned lunar base or a Lagrange-point spacecraft? Hardly! They can't move, being fixed in the one case to an inconveniently immovable planetoid, and being held precariously in a highly unstable gravity-momentum eddy in the second. They are precisely sitting ducks. This, incidentally, was the main reason why the military rejected your idea years ago.
Would redundancy save an lunar base or Lagrange-point spacecraft? In the case of the former, you could argue that your hypothesis allows for six redundant lunar bases -- one for each of the successful Apollo missions. However for the cost of each one of those -- and remember how much you tried to argue those things cost! -- you could deploy 3-5 equivalent low Earth orbit missions. The monumental nature of an Apollo mission naturally precludes any effective redundancy.
And there can be no practical redundancy for Lagrange-point spacecraft because of the constraints of that location. The unstable ones simply can't have spacecraft in them at all, and the stable ones are accessible only through halo orbits that will become crowded.
So in your system there is a limit in terms of both environment constraints and cost to how much redundancy can be achieved. But for the same cost you can put many more spacecraft in Earth orbit where the constraint does not exist.
There is no property of a lunar-surface installation or Lagrange-point spacecraft you have named that cannot be satisfied better, cheaper, and less vulnerably by an artificial spacecraft in Earth orbit. All the arguments you cite for the use of satellites in military operations are for
satellites, not for the Moon.