Help with dyeing Roman blinds

Hello all!

I’m hoping that someone has some experience with this
that they can pass along to me. I am painting most of our new house and I love
the blinds but want to change the color. They are beige right now and I’d
like to dye them a soft sage green to go with my color palette.

The blinds have
thin wood (maybe bamboo?) horizontal pieces woven with fabric threads. Does
anyone have advice on dyeing these blinds? Should I use something like RIT dye
or is there something better?

Any advice would be very much appreciated!

…angie