I think the answer to this question is open for debate, as it depends on a lot of factors.
To start with an extreme, King Tutankhamun died about 3,000 years ago. The opening of its burial grounds was attended by Lord Carnarvon, a British sponsor of archaeology in Egypt, who died shortly after attending the tomb's opening. While at first it spawned superstitious beliefs like 'Tut's curse', nowadays researchers believe it was, perhaps, caused by various bugs found in the tomb, namely Aspergillus niger and Aspergillus flavus. These molds can cause allergic reactions, including lung bleedings. The toxins can be particularly harmful for people with a weakened immune system. Other bugs, like the respiratory-assaulting bacteria, Pseudomonas and Staphylococcus have been found as well on the walls of the tomb (source: National Geographic).
However, food items were stored alongside a host of other sacramental stuff, so Tit's tomb was anything but a 'clean' grave. A normal grave hence may, or may not lack these contents and hence its bugs. However, there are many, many more variables in play, among them the type of coffin used to bury the corpse, the type of grave, type of soil, humidity, temperature etc. etc., which all interact and can affect the duration of the various stages of decomposition (source: Wikiepdia). Up until the last phase (skeletal phase), active decomposition is taking place, and hence many bugs are around, which would raise hygienic issues.
Lastly,cleaning up graves is quite regularly performed, and a period of four decades is used on a regular basis (source: BurialPlanning.com).
In all, I guess a definitive answer to this question doesn't exist, other than longer than 3,000 years....