...would anybody in their right mind risk going forward with a mission like that?
Yes. And before you present another wall of ignorant text, please explain exactly what your professional and academic qualifications are in regards to space launches. Sorry, but unless you can demonstrate some actual experience in operating a spacecraft, I don't think the world is compelled to give a rat's hiney what you personally would do in some situation.
The thing gets hit by lightening. This is a moon landing mission. Men's lives are at risk, at stake, big time.
Airliners get hit by lightning all the time without needing to make an emergency landing. In that case there are more lives at risk, and the lives in question have booked routine passage expecting the air carrier to take all due precautions.
In the case of Apollo, the crews were highly trained, highly experienced test pilots who had been informed of the risk, were knowledgeable in the risk assessment, and who were accustomed to flying dangerous missions voluntarily.
Are you as a flight director, or Apollo Program director, seriously going to allow the thing to go forward?
Absolutely yes.
The CSM was affected, but the Saturn V launch vehicle was not. The launch vehicle was in control and was flying normally under power. In that situation: absolutely yes, you continue the ascent as planned. This is because ascent under power is a high-energy, changing-stage condition. In contrast, orbit is a low-energy, steady-state condition. "Aborting to orbit" is far preferable to trying to abort under power. If the launch vehicle is sound and can deliver the spacecraft to a stable orbit, then an abort may be decided subsequently, and would occur in the form of an SPS de-orbit, which is a far safer thing than an LES abort.
How do you know after the thing is hit by lightening that there is not some relatively subtle problem...
Because there's no indication of any. How do you know, getting into your car, that there isn't today some subtle unindicated failure waiting to kill you? Real flight directors differ from your hysterical caricature by basing their decisions on actual data, not on unsubstantiated suspicion.
Lightening could cause that, easily.
The normal operation of the launch vehicle could also cause any of that too. By your logic every launch would need to be aborted -- not just for the indication of failure, but for the suspicion of some unindicated failure.
You would abort the mission in the sense that you would bring the astronauts home as quickly and as safely as possible...
Nope. You don't abort during powered ascent unless it is the launch vehicle that is at fault. An LES abort is extremely dangerous. You attempt it only when the alternative is certain, immediate death.
The equipment that was affected by the lightning strike was redundant. Two units were provided, where only one was needed. There was a perfectly good signal conditioner ready to be used.
You err in assuming there was no way to validate the spacecraft for the remainder of the mission. In fact that's why the mission profile always called for an Earth parking orbit prior to TLI.
The equipment must all be working perfectly to carry out LOI, DOI, landing, ascent, lunar orbital rendezvous.
Hogwash. The Apollo system was designed specifically for redundancy so as not to require a perfect spacecraft in order to fly a successful mission. In fact all Apollo missions except for Apollo 17 encountered a significant failure. A significant number of airliner flights encounter a failure of one kind or another. Aerospace engineering is precisely the art of engineering for graceful degradation.
You have no clue what you're talking about.
Apollo 12 is fake, right there...
Nope. Once again you've amply proven that you will shoot your mouth off ignorantly about things you don't even vaguely understand.