we allowed to conduct and we are not allowed to conduct or we were allowed to conduct and we were not allowed to conduct, which is right? thx

I hope I understand which sentences you are asking about; I'm guessing you mean "We allowed to conduct and we are not allowed to conduct" vs. "We were allowed to conduct and we were not allowed to conduct." If I'm right, then it would seem somewhat strange to say a sentence like "We were allowed to conduct and we were not allowed to conduct" which seems to contradict itself, but anyway this sentence is correct grammatically.
"We allowed to conduct and we are not allowed to conduct," on the other hand, looks to be incorrect since it appears to be missing the auxiliary "are" before the first occurrence of the past participle "allowed" in the first clause; in other words, like your second sentence I'm assuming you meant the verbs of both clauses of this sentence to be passive, i.e., "we are allowed . . . we are not allowed."
Another reason I suspect that an "are" is missing from the first sentence is that the verb "allow" is transitive, meaning it always requires a direct object. That is, we can say "We allowed him to conduct" or "We allowed the guest to conduct" using the simple past tense form of "allow" and the direct objects "him" and "the guest" followed by the infinitive "to conduct," but since there is no direct object mentioned anywhere in your sentences, I have to assume you meant the first "We allowed" to be passive, and thus a form of the auxiliary "be" must be used here, presumably present-tense "are" to be parallel with the second clause of the first sentence, "we are not allowed."

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