Translation:My mother is very gullible but my dad is not.
It acts like "to be" verb. I mentioned somewhere that Vietnamese does not really use "to be" (thì/là/bị/ở) but in some cases, this kind of verb is necessary to distinguish subject and object.
What’s the difference between the four?
This should take a while to explain, but in short:
thì: usually used in second clause of a sentence, showing the opposition (e.g. you are happy and I am sad - bạn vui và tôi thì buồn). It can be combined with nhưng or tuy nhiên.
là: used when saying something is being something (job, object, species...) (e.g. tôi là một bác sĩ, đó là một con mèo)
bị: used with passive voice in a negative sense (anh ấy bị giết - he was killed), in contrast, "được" is also used with passive voice but with positive sense (tôi được tặng tiền - I am rewarded with money).
ở: to be at a location.
Wait, there’s no copula in the first clause in the first sentence...
yes, as krikori said, the copula is unspoken. however, note that là only links the subject to a noun or a noun phrase, never to an adjective.
It's the unspoken là between the subject and adjective.
Bạn (là) vui