全く筋が通っていない。私は酔っぱらって外で叫んでいたわけじゃない。

。。

That makes no sense at all. It's not like I was out there drunk, shouting in the street.

Literal

Completely logic [subject-が] pass-[negative-resulting-state-ていない]. I [topic-は] get-drunk-[て] outside [at-で] was-shouting [nominalizer-わけ]-not.

筋が通る is a set idiom 'logic passes through' = 'to make sense, to be coherent.' ~ていない on this state verb marks the ongoing condition of not-making-sense. わけじゃない ('it's not the case that ~') is the softening denial pattern used to push back against an assumption or implication, rather than denying a fact outright. The speaker is rebutting an accusation by reframing what did or didn't happen.