I measure "trust" by actions, not words. When you buy a product, you aren't just saying you trust it, you are trusting it. Trust is a verb, not a state of being.
Unless you are very unusual and are completely off the grid, you've probably solved the question of how you personally decide how to trust a wide variety of commercial agencies of highly varying degrees of regulation and highly varying degrees of life-threateningness. Possibly without realizing it. In theory it may be unsolvable, in practice it doesn't seem to be.
It should be pointed out that this isn't theoretical, either. People die because the FDA forces them to not take drugs, even when death is essentially assured in the short-term anyhow. It's a well-known problem. If the FDA was more advisory, I suspect it would be a net good. I really can't imagine people en masse running down to WalMart and buying Dangerousol (now with twice the danger!) any more than they manage to now. (Which you can't ignore either, the FDA is not perfect.)
I think ultimately it comes down to how much deregulation occured.
If you go all the way and the FDA was replaced with companies who offered to test and "approve" drugs for profit then I think it is difficult to establish a full trust relationship with those entities.
You mention the FDA becoming advisory; that could become a good compromise. However there is a danger that people would simply ignore the dangers and, at some point in the future, suddenly realise they had done something terrible to themselves :D
A balance is crucial; I think we actually have it in the drugs industry, but perhaps there is room to make modify as well...
but you have no choice but to accept them as the entity whose recommendations you follow with regard to drugs
What features are included in a car is regulated by competing companies and you can pick which set of choices you deal with.
The competition between companies and the choices that you have imposes a discipline that does not exist with government.
With the government, you are simply coerced to accept their judgements. Which are influenced in all sorts of ways by the drug companies.
And if something becomes glaringly obviously wrong with something the government is doing, fear not. In a decade or two, someone will get around to changing it.