Place chicken, taco seasoning, tomatoes with juices, salt, chicken broth, and green salsa in Instant Pot.
Set to manual mode and cook for 10 minutes at high pressure.
Allow pressure to release naturally (about 15 minutes), remove and shred the chicken. Set aside.
Stir softened cream cheese into the soup in the pot and whisk until fully melted into the soup.
Return chicken to the soup and serve with diced avocado and Monterey jack cheese.