Your circuit appears to be designed to give a "hard count" from 0 to 7 and each bit drives one of the primary colors. So, we would expect that as it counts from zero to seven, it will give you these "hard" colors:
0. dark
1. red
2. green
3. yellow (red + green)
4. blue
5. magenta (blue + red)
6. cyan (blue + green)
7. white (red + green + blue)
In order to "smoothly blend" from one color to the other, you must have something more than "hard on/off" control of your LEDs.
Typically, that means using pulse-width modulation (PWM) to vary the apparent intensity of the LEDs.
While you could do PWM without using a microcontroller, it would be enormously complex, expensive, difficult, and fiddly.
Using a microcontroller, OTOH, is simple, cheap, easy and foolproof.
It appears that your design goals are at odds with your desired outcome. You can't have it both ways. Select one.