Neutral and ground need to be separated at the subpanel. Neutral on a neutral bar which is isolated from panel chassis, and grounds on a ground bar attached to panel chassis. The subpanel needs a 4-wire feed. This may seem absurd since they go to the same place, but don't do what Great Britain does and try to combine them! Your GFCIs will laugh at you if you do.
Neutral and ground are bonded at the main panel, or to be more precise, at the first disconnect past the meter (where ground rods also come in).
Here is my yes or no questions. Can I simply run the main panel off the grid and the sub panel off the generator at the same time? Is there any issues with the neutral being connected between the main panel and the sub panel?
With that type of generator interlock which switches hots only? YES - however, on your auxiliary generation equipment (generator or solar), neutral and ground must be isolated.
Remember the rule where the supply must be bonded? Many portable generators and solar inverters e.g. "solar generators") have neutral-ground bonding, in the service of that worthy goal. The problem is, they can't be used on your type of "non-neutral-switching" interlock, unless they provide a procedure for un-bonding neutral and ground.
I understand that this works well with the main panel turned off (main breaker off) but the neutrals are still connected to the grid.
That's fine, though. It takes 2 wires to complete a circuit. If only 1 wire is connected, no circuit!
Here. As a thought exercise, imagine you pull the neutral-ground equipotential bond in your main panel/disconnect, and replace it with a heavy 2 volt transformer so that your ground is pushed 2 volts away from neutral. (but that transformer can flow 10,000 amps of current momentarily, so breakers will still trip and the system will work fine). Now referencing from ground, your L1/N/L2 voltages are 122V, 2V and 118V.
Remember the part where I said neutral and ground must be isolated on the solar and generator? If they're not, we are shorting neutral to ground creating a 2 volt dead short - that's obviously bad.
But if they are isolated, then simply the generator chassis is at 0 volts, the generator neutral is happily at 2 volts, and hots are at 117V and 113V (let's say it's a 115/230V generator). Everything is fine!
What about a neutral-ground short? Generally becuase we did not actually put a 2V transformer there, it's not a terrible thing. However if the generator or solar has GFCI protection on its output, that will trip the GFCI. Note that you cannot backfeed a GFCI breaker, so don't go thinking "Aha, I'll replace the generator-side breaker in my subpanel with a GFCI". If you wanted to retrofit GFCI to the solar or generator output, you'd need a standalone GFCI in a 2-space panel of its own.
This scares me as to protect the solar equipment. Can this be done? Any risk have a shared neutral? I will never be able to back feed the main from the sub with the transfer switch, but the neutrals are keeping me up at night.
Just think about the mental exercise of "replace your neutral-ground bond with a magic 2-volt transformer". If everything there checks out, then you have the isolation you need.
Why do we care? Several reasons but here's a big one. Faults throw huge amounts of current between neutral and ground. If there's a difficult-to-detect problem in your panel, that current could path via your generator's ground wire, out to the generator, via the generator's neutral-ground bond, back out the generator's neutral wire, and back to the utility. Since none of these are either switched nor breaker protected this could start a fire. The solution to this problem is either a transfer switch that throws neutral (Canada has subpanels that do that), or isolate neutral and ground on auxiliary sources.
