Without wishing to go into deep theological reasons why, I don't think it matters if you step on a grave (as long as you don't damage flowers or anything that may be on it ?) The person who once was, isn't there any more ... just their 'wrappings' so to speak ?
I think all graveyards and cemeteries should be treated with respect, but only for the sake of the living ... just as one should respect other peoples houses, cars, children, etc.
Maintaining country church yards is a bit different ... they are so often havens for wild flowers, birds, insects ... then mowing them and keeping them as tidy as town cemeteries can amount to destroying useful habitats for wildlife ... our local one is well maintained, but not until the wild daffodils, cowslips, cranesbills, orchids, yellow rattle, etc. have all set seed.
