Awhile back I asked the company if Titebond II could be colored. The reply was, yes. Apparently about any dye can be used, including Rit. I use Titebond II for 99.99% of all my gluing, and even thin it for finishes on my canes and such. Haven't had anything I wanted to color/dye for awhile, so haven't tried it yet. I'll probably thin the glue first, and, of course, try it on scrap wood first.
An aside, I use acrylic latex paint on various projects. Thinned some down a few years ago, and it comes out like stain, all the wood grain shows, nice. Somehow a cane handle I'd 'stained' with some got lost outside my shop, and was out there, on the ground for over a year. When I found it, was still in great shape, red on one side, black on the other. Probably still got it out there, somewhere.
When I do get around to trying the colored Titebond I will likely use the latex paint to do it, then I can mix whatever custom color I like. I have found that I need black, dark green, dark blue, white, yellow, red, to be able to mix colors properly. No matter what they teach you in school, with just the primary colors, you are not going to get a proper green, blue, or whatever.