Learn Farsi: ماست سفید است.

Uncountable nouns used in a general sense, like mâst, don't need any special markers in Farsi. This matches English grammar perfectly. Even if you meant "the yogurt" (a specific batch), it would still be just mâst here, because Farsi doesn't have a direct equivalent for "the" when a noun is the subject.

I usually hear Iranians attach the verb to the adjective. How is this pronounced in everyday spoken Farsi?

In casual speech, the formal ast shrinks to the suffix -e and attaches directly to the word before it. Because sefid ends in a consonant, you will almost always hear this spoken as mâst sefide.

Since the meaning is obvious, can we ever drop the verb ast entirely?

No, Farsi strictly requires a verb here. While some languages let you just say "Yogurt white," in Farsi you must include ast (or the spoken suffix -e) to link the subject to the adjective describing adjective.