We see it often enough. Red eyed monsters, ghosts, robots, etc. Media monsters are made to be creepy and unsettling generally. So there must be a bases for them to have this trait.
I know red has a natural psychological effect, it grabs attention quite easily. So would it benefit a creature who's purpose was to terrorize, or otherwise frighten the enemy or prey?
There are several very precise reasons to design red into anything you want someone to be afraid of.
It's worth noting that a human seeing the color red experiences two interesting things: Increased heart rate and increased adrenaline flow. The increased blood flow is a reaction to our association with red and it's common social meanings. When people are angry or embarrassed, their faces may flush red. Given that these are both indications of negative social situations, we learn to associate deep red with negative contexts. Furthering this, red is the color of blood, and visible blood likely means injury of some sort has happened. Since our animal natures would rather avoid injury, blood-red colors tend to intimidate our sense of safety.
(Note: There are also positive contexts for red colors, as in sensual use or sport, but these are beyond the scope of a "creepy monster" situation.)
Consider also that red is the color of fire. Fire, as all prudent humans know, is dangerous to touch. At the very least, you'd want to be cautious when handling fire. However, when fire grows out of control, your tendency would be to run from it so as to avoid painful outcomes.
From the evolutionary perspective, many poisonous animals use red as a way to signify that they are dangerous. Many snakes, insects, and fruits use this tact to either directly demonstrate danger or imply danger. The animal inside all humans therefore sees red as a potentially poisonous color, and thus will try to avoid it in already negative contexts.
Physiologically, When you see red, your brain will examine the thing its attached to and, most likely, prepare your fight-or-flight response by increasing your heart rate and adrenaline levels.
On a purely physical level, this will lead to heightened emotions. Assuming you are currently a little freaked out - because whatever situation has put you in the direct gaze of a creepy being would freak you out - seeing red eyes will undoubtedly raise your hackles and cause some intense feelings, likely even outright fear.
There are many excellent reasons to use the color red in eyes for intimidation and fear purposes.
Yes. As the old saying/cliche goes: "The eyes are the gateway to the soul". As humans, we are programmed to make eye contact (fun fact: we are the only animals whose whites of the eyes are always visible).
Due to this eye "fixation", eyes are often used to communicate significant changes to the character e.g. pupils shrinking/expanding or the iris changing colour. We are also prone to noticing if something is "wrong" with the eye, like being bloodshot or if they are blind.
