I would wager that it's perfectly fine.
I've spent some time in Indonesia where this is also common. I'm not dead yet lol.
Think about the millions of people in countries where the bathroom situation is like that. They live their lives like that, and have been doing so for a very long time. If it were a huge issue there would have been changes in their lifestyle to accommodate for that.
I'm not 100% on the differences in Indonesia and India, but at home there was soap so it was immediate washing. Out in public their either was only facilities for peeing, or if they did have toilets or a place for pooping, there would be a sprayer to wash off with so you didn't need to use your hand. Or if you got lucky they would have a sit down toilet with tp.
Edit: I see you mentioned not caring for personal opinion. Sorry about that, but realistically I doubt there's much need to worry considering the millions of people that live like that. If it was an issue they wouldn't live like that.