I looked at the Siskel and Ebert review, which was during the theatrical release, and the hospital chase, the T-1000 entering the helicopter, and a couple other scenes that weren't blue in the trailers are blue there. And the "You can't just go around killing people" scene also has the blue tint. (Yes, it looks purple, but that's due to incorrect hue setting at some stage between the film-to-tape transfer of the footage and the digital file on that site - either in the telecine, video post, the VHS recording or the VHS-to-digital rip.)

Those blues seem in line with Cameron's sensibilities - I can't believe that Cameron would sign off on a non-blue color timing, it would go out to theaters that way, and then he would change his mind and extra money would have been spent to completely retime the film just for home video a few months later. I would understand if the blue timing had been introduced in the Special Edition extended cut, but no, it's there in every home release of the theatrical cut too.

I think the most logical explanation is that the final color timing hadn't been done when assembling the trailers, and that the blue is consistent with what showed up in theaters in 1991.