Answer:
There should be no conflict between economic growth and equity. Some conflicts may arise, since generally economic growth benefits the richest more than the rest of the population, but government policies can offset this situation, and the living proof are Scandinavian countries.
The theory that leads to conflict is the trickle down effect (supply side economics) since it advocates for allowing rich people to get so rich that they will eventually realize that the only that they can get richer is by distributing some of their wealth. That never happens.
Supply side economics, and all other variations of classical economics, monetarism and neo-classicism are great in theory, but they have never worked in real life.