I am irreligious and athiest. But I still trust Ramakrishna Mission and I think you can specify that you don't want your money spent on religious activities.
Just so you know, Akshaya Patra is also part of ISKCON, the Harekrishna people in the US. They are headquartered not far from my home, and they are trustable in this regard.
[0]: https://www.telegraphindia.com/west-bengal/calcutta/ramakris...
[1]: https://www.thehindubusinessline.com/news/national/hero-moto...
[2]: https://theshillongtimes.com/2021/05/20/rkm-sohra-endeavours...
[3]: https://m.timesofindia.com/city/kolkata/60-bed-safe-home-set...
[4]: https://m.timesofindia.com/city/visakhapatnam/ramakrishna-mi...
Just so you know, Akshaya Patra is also part of ISKCON, the Harekrishna people in the US. They are headquartered not far from my home, and they are trustable in this regard.