Any way to make plot points in scatterplot more transparent in R?

Otherwise, you have function alpha in package scales in which you can directly input your vector of colors (even if they are factors as in your example):

library(scales)
cols <- cut(z, 6, labels = c("pink", "red", "yellow", "blue", "green", "purple"))
plot(x, y, main= "Fragment recruitment plot - FR-HIT", 
     ylab = "Percent identity", xlab = "Base pair position", 
     col = alpha(cols, 0.4), pch=16) 
# For an alpha of 0.4, i. e. an opacity of 40%.