While this may be a post hoc explanation the Arnie Terminator variant was one of many variants, Skynet basically had an infiltrator with basically any race, ethnicity, build, or sex. Though I believe the Arnie variant was simply the most common/ oldest version that Skynet had, which mind you still makes Kyle Reese a dumbass but it does make it slightly more forgivable.

Also who knows if he ever encountered an Arnie Terminator before what with the timelines slowly getting increasingly fucked in each subsequent loop, plus who knows what he knew of the old world since the dude was a soldier in a post apocalyptic conflict who may have been a kid or even unborn when the nukes went flying. For all he knows weird Arnie looking dudes being sus was normal.