Explanation:

The Muslim League opposed the Quit India Movement as it was of the view that if the British left India in its current state, Muslims as a minority would be oppressed by the Hindu majority.
Hindu nationalist parties like the Hindu Mahasabha openly opposed the call for the Quit India Movement and boycotted it officially. Vinayak Damodar Savarkar, the president of the Hindu Mahasabha at that time, even went to the extent of writing a letter titled "Stick to your Posts", in which he instructed Hindu Sabhaites who happened to be "members of municipalities, local bodies, legislatures or those serving in the army...to stick to their posts" across the country, and not to join the Quit India Movement at any cost.
The RSS, under M.S. Golwalkar refused to join in the Quit India Movement as well. However, such a non-committal attitude during the Indian freedom movement also led to the Sangh being viewed with distrust and anger, both by the general Indian public, as well as certain members of the organization itself.
The Communist Party of India was banned at that time by the British government. In order to get the ban lifted, as well as to assist the Soviet Union in its war against Nazi Germany, it supported the British war effort, despite support for Quit India by many industrial workers. In response the British lifted the ban on the party.