This article is from the The Terminator FAQ, by Karsten A. Loepelmann firstname.lastname@example.org with numerous contributions by others.
Several possibilities have been discussed:
1) Dogs may have to be "trained" to sniff out Terminators. This implies that
John's dog Max was just barking for the hell of it when the T-1000 kills
John's foster parents. Not very likely.
2) Not all dogs bark at Terminators. Unlikely.
3) The dog at the desert hideout also did not bark at Sarah or John; maybe the
dog didn't bark at "Uncle Bob" because it knew Sarah and John.
4) JC intentionally neglected to have the dog bark, to show that the
Terminator was becoming more human. Quite possible.
5) It's a continuity glitch. Live with it ;-)
6) Lastly, the unfilmed Gant Ranch Sequence in the Annotated Screenplay notes:
The dogs do not dig Terminator at all. They are barking and whining,
slinking around, keeping their distance.
Thus, the reaction of dogs to the Terminator was not forgotten. It is
likely that showing the dogs becoming alarmed with the "kinder, gentler"
Terminator would have confused the audience ("Is he a *good* guy or a *bad*
guy?"). Some people are slow.