Blame Bo Diddley for educating an entire generation with the song, who do you love.

That song has had many covers but my favorite is a local band, The Woolies, that had a Billboard top 100 hit with it in 1966:

https://www.youtube.com/watch?v=SfgmaNPJXZo

to this west coast usian ear, 'whom do you trust' sounds hopelessly antiquated and pedantic.

It sounds like proper English.

OK, this isn't the most scientific thing, but 'who do you trust' brings up 400K results on Google, while 'whom do you trust' brings up 150K, and the first result is an article on exactly this topic(1).

So obviously what's "proper" or not depends on what dialect you're trying to conform to. I can believe that if you're part of that narrow, elite sliver that would naturally use 'whom do you trust', the "incorrect" use of "who" as the object of a sentence must seem garish, but to the rest of us, trust me, "whom do you trust" sounds ridiculous.

Live and let live?

(1) "Whom do you trust?" http://www.economist.com/blogs/johnson/2012/04/grammar

I agree with thee; thy position is sound.

I thought whom follows a preposition: To whom is the message addressed?

The distinction is not whether a preposition is involved or not, it is whether the "who/whom" word is operating as an object ("whom") or a subject ("who"). That's why delinka's mnemonic also works.

In both "to whom is the message addressed" and "whom do you trust", "whom" is an object, not a subject.

All that being said, it is increasingly a common and acceptable practice to use "who" as both an object and a subject, so it's probably not worth losing too much sleep over.

The mnemonic I got in school was that if you can answer with "him" then it should be "whom."

Who made this? He made this. Whom do you trust? I trust him.

This mnemonic is predicated on answering in complete proper sentences. I realize that in current colloquial English, "Who made this? Him." is certainly an exchange one might encounter.

The pronoun is in dative case, or even if objective case, the test works of "whom" because "I trust her/him" and not "I trust he/she".

Just FWIW, it is not in the dative case. The dative case is only for indirect objects (which follow pronouns), or direct objects specifically related to the act of giving. Trusting is not giving, and there is no prepositional phrase in this sentence, and so the pronoun is a direct object. But yes, it still passes the test for whether it's objective or subjective.