update cell value based on result from 2 other cells value

So i have a table looking like this:

table1

id   name    dad    mom    color
1    bob     12      4      NULL
4   embla    NULL   NULL    blue
12  clyde    NULL   NULL    blue
2   anna     12     4      NULL

I would like to SET anna & bobs color based on their parents color. It might not alway be blue..

Im not very good at this but ive tried to alter another code i used for something else but that didnt work :P

   UPDATE table1 AS p 
   INNER JOIN table1 AS Dad
      ON p.dad_id = dad.id AND p.mom_id = mom.id
         IF color = blue
SET p.color = blue
     .....?

this is how far i get and where i struggle... as i dont know how to check for the parents color and then return the same color to the offspring...

So i want to set the same color as their parents in the color column, and if the parents color do not match i would like it to be NULL.

I dont have many colors to choose from so i can use the value "blue" i the code. i dont need to actually "match" the color value, i can use the value blue, red or yellow and run the script 3 times.