Evolutionists use to say that most of our genomes was junk DNA. This was to highlight that design was mostly simple and therefore can be explained through a chance and random process that comes mostly from an error in the copying of what is already working to make better and more complex life. But now scientists are finding a lot more function in the so called junk DNA and many evolutionists have resisted the evidence along the way. This is the same more many aspects of life and slowly but surely we are beginning to see the great complexity yet orchestrated design in things from even simple organisms to the finely tuned universe that is designed for life.
Natural selection does and can work with intelligent design. Its the capacity that its given that is in dispute. Creatures have the ability to adapt and change to conditions they encounter in their environments. But those changes come mostly if not completely from a genetic ability that is already there. This is where the so called junk DNA may come in. Maybe there is a lot more capacity for creatures to draw on their existing genetics to change and switch on and off genes or recombine their existing genetics to bring about those changes. But those creature primarily remain as they are but have a great capacity for variation. They dont turn into other creatures and all living things didn't come from a common ancestor.
In fact evidence shows that there were many lines for where all creatures come from and that the genetic capacity was there from a very early point in the scheme of things. Too early for that complexity to have evolved from a gradual process that has very rare beneficial mutation for the amount that would be needed to just make small changes where several mutational changes are needed at the same time.