This is a very useful resource for verbal conjugations in Russian:
There are no difference between "present simple" and "present continuous" in russian. There is just present. So you can say птицы пьют молоко to describe either current action or general fact. The only way you can differentiate current action from fact is by adding сейчас(now) to the sentence.
The birds are not drinking milk
Птицы сейчас не пьют молоко.
Out of sheer curiosity, if a sentence like this were to arise and be said only with the intent of meaning "Birds do not drink milk" (as opposed to also icluding the possibility of "The birds aren't drinking milk"), would it be better to say "Птицы никогда не пьют молоко" to remove any possible ambiguity? I know that that translation means "Birds never drink milk", but if one were to follow what I said above (about saying "Birds do not drink milk" without the intent of the other present tense as a possible translation), would saying the sentence this way be better, or am I reading way too far into semantics and just mucking things up in my head for no good reason?