RIT dye actually contains two types of dye: a direct dye for cotton and other cellulose fiber, and an acid dye for wool, other animal fibers, and nylon.
On cotton, RIT dye needs heat to be properly set and even when properly set will still bleed in the wash unless a dye fixative is added, which pretty much cancels out the convenience or rit considering that the fixative is only available at dye supply places. Fiber reactive dye such as procion mx, or dylon (cold water or permanent) don't need to be heated to set and are fast after the excess dye is washed out.
On wool, the dye can be used just like any other acid dye, with heat and an acid like vinegar. The dye water won't completely exhaust though because of the direct dye.
The type of acid dye used in RIT is a levelling class dye and not as washfast as some other acid dyes such as jacquard and may bleed a bit in the wash.
I feel however that I must mention that alot of dyes that many handspinners and dyers swear loyalty to (ashford, cushings, gaywool, landscapes) are also leveling dyes; they might not contain they same exact dyes, but they work in similar ways.
You didn't mention what the fiber content of your yarn was. If it's cotton, I'd suggest you'd buy some fiber reactive dye, but if it's wool, or other animal fiber, then I'd say give it a shot.
Just remember when dyeing to use gloves and dedicated dyepots and utensils.
I would assume that the RIT dyes would be more washfast overall than food coloring but since food coloring is not tested for it's use as a fabric dye, it's hard to know.