No, an old cesspit is not a problem; feces are not a pollutant - if anything, they are fertilizer.
I would talk to the neighbors; it is not very likely that your building gap is any different from the adjacent properties. That would be enough for me.
If the neighbors built with a white tank, you will need one too, and if the neighbors had to use piles or had to fill in an especially thick layer of gravel, you will have to take that into account as well.