I believe the red gate is red due to its relative recency. There is no real evidence to prove or disprove this, but my thoughts are that the color of the gate is indicative of its displacement... However, since all of the gates are a fair number of centuries displaced, they all seem to be the same color. Essentially they go from infrared (no time displacement at all) to ultraviolet (a portal directly to the End of Time/Darkness Beyond Time, and no I'm not implying they are the same, but simply that the gate would lead to one of them.)
Since infrared is invisible to the naked eye, it is a fitting description for the normal flow of time. Since the End of Time is theoretically after infinity, it too would need an invisible gate.
Note: the gate in 2300AD was not a gate to the End of Time, but rather the conservation of time redirected it there.
Has anyone considered how Robo may have played into the red gate's existance? I'll need to think more on it before I come up with a basic theory, but it could be that there are gates everywhere, and possibly Robo detected that one by chance?