In ancient mythology we see a natural meaning of the color red that would surprise nobody. Historically red often represented violence from blood, or life in blood (i.e. punishment for sin in the life of another). For example, Sekhmet was a warrior goddess in ancient Egypt:
She was envisioned as a fierce lioness, and in art, was depicted as such, or as a woman with the head of a lioness, who was dressed in red, the colour of blood. (Wiki article).
As sacrifices were used to appease the wrath of gods among pagans as well as within Israel, the violence was averted by shedding of blood. For example with regards to the 'red heifer':
The early Jewish conception was that the sacrifice of the red heifer was an expiatory rite to atone for the sin of the golden calf. The color of the heifer, as well as the scarlet thrown upon the fire, represents sin (comp. "your sins be as scarlet"; Isa. i. 18). (Jewish Encyclopedia)
This historical sense of red, with reference to religion is not enough. We need to look at the more recent history surrounding the event. Naturally the spies would have it fresh in their meaningful history that 'destroying angel' (Exodus 12:9) that just recently killed those not protected by the blood on the door posts of their homes. Therefore when a red rope was to be in the window of her home, protecting them from the destroying army of Israel, the imagery must be correlated, if any respect to history is to be had. Although blood does not stay red, is very besides the point. We all think 'red' when we think 'blood'. There can be no doubt about this relationship in the recent history.
On a practical note the red rope would be something easily visible to ensure soldiers did not kill those inside and it. Possibly it was previously used for prostitution for the same purpose. That Rahab's house or brothel (whatever it was) was connected to the wall surrounding the city, making it easy to let down the spies over the wall, may have also been convenient for 'extra cautious' men using her services. However, the practical aspect of the red color does not intrude upon the meaning in the religious wider context.
There is strong evidence that red therefore represented the same protection of violence by blood, as just experienced by Israel by at the passover. This means the salvation of Rahab was salvation from God. The fact that whoever went outside the door of Rahab's home, that 'his blood should be upon his own head' further enforces the 'red' meaning.