You could try disabling scientific notation, but I think a better thing to try the scale_y_continuous() function, and using the labels=comma argument from the scales library.
First import the scales library (on top of ggplot2) :
library(scales)
^install if needed
For clarity, let's say you save your current ggplot to the variable plot:
# your current plot
plot <- ggplot(data = budget_genres) + geom_bar(mapping = aes(x=reorder(genre_1,avg_genre_budget, Fun=mean), y=avg_genre_budget, fill=-avg_genre_budget), stat = "identity", Fun=mean)
You could try adding the scale_y_continuous() function to the plot like so:
# the incremental change to the y axis
plot + scale_y_continuous(labels = comma)
Not 100% sure this will fix the issue but I think it probably would.