Whether it is a profit making organisation or non-profit organisation, principles and practices of management do not change. Secondly, in either organisation people work. Therefore, people issues also remain same. To drive the organisation to attain its goal, optimum utilisation of the resources is also important. Against this backdrop, MBA course with whatever specialisation you do is important.
In commercial organisation, while influencing customers to buy a product/service is important. In non-commercial organisation influencing the people or organisations to donate funds is important.
I would like to keep HR, Marketing and Operations in the order of priority. While MBA (Ops) is quite interesting and challenging, the subjects like Production Management, Materials Management, Supply Chain Management, Production Scheduling may not be that useful considering your past career.
All the best!