Is this a valid reason not to drive my car?

Of course it’s a reason. It’s also illegal in this state to blow that white smoke.

That’s going to depend on the specific decider and their rules, but I would say ‘yes’, that blowing your head gasket is a legit reason to not drive your car. I wouldn’t even get into all the nonsense about the environment unless they ask. If they do, I’ll bet they would accept the environmental issues as legit too, but I feel like you don’t even need to get into that level of detail with them.

I personally would not drive it.
Since a head gasket acts as a seal, the moment it blows there will be an immediate loss of pressure in your engine. This loss of pressure means the pistons in the combustion chamber will no longer be firing with force, and you will feel a significant loss of power
No longer pressurised within their dedicated passageways, oil and coolant will then start to leak into areas of the engine that they do not belong, such as the combustion chamber. The coolant may then mix with your motor oil, diluting the oil and reducing your engine’s ability to properly lubricate important parts of your engine, such as your cam shaft or crank bearings. Without the proper lubrication, this will quickly lead to bearing damage, and the need for an engine rebuild.
Additionally if the coolant is leaking, then it’s no longer available to cool down the engine. Without this support, the engine will soon overheat if you keep driving – leading to further cracking and damage to your engine

Have you checked your oil? I had a blown head gasket once, and when I removed the oil filler cap it was covered in a mayonnaise-like substance. It’s an emulsion formed when water leaks into the oil. So no, I wouldn’t drive it.

may contribute to the mixing of technical fluids, their entry into the combustion chambers or the occurrence of exhaust gas leakage. All this negatively affects the operation of the power unit, its environmental friendliness and fuel consumption.

Your truck has had some very serious engine damage and it will only get worse. Park it until you can get it fixed, and then have it towed to the repair shop because the antifreeze will fill a cylinder and starting it, or trying to, may only cause more damage.

What you have is the barrier between coolant and engine (including oil) is compromised. What you are seeing is mainly water vapor with the coolant chemicals in it. Bad enough. But what you also have is coolant getting into your oil. The oil is being diluted and losing viscosity (not lubricating any more). You also have water in oil in a churning environment. You are creating a sludge akin to butter in your engine. Yes, you can continue to drive this car but it is 100% guaranteed your engine will eventually seize up costing you more than the car is probably worth. Depending on the value of the car you might want to cut your losses, drive this beast to the junk yard, get your $250 and go get yourself another vehicle.

If coolant is getting in the oil you take a great chance at spinning a bearing, among other things.
If the vehicle is worth anything you might not want to drive it and get it fixed if it is just a beater then drive it till it croaks and walk away.

Please look at your oil dipstick. Is the oil level rising? Does it look frothy?

When the engine is cool, open up your radiator cap and look inside. Does the antifreeze look like a milk shake? Oil mixing with antifreeze will do that.
If you value the vehicle you need to get it fixed.