I personally disable all updates; themes/plugins/core, too many times I was burned with erros in the most inconvenient times possible.
Now I do manual updated for each site after I checked in a development environment. after im sure that everything works and I fixed every bug that happened I update the live site.
Now I have far less problems.
The down side is that updated provide the latest and greates (usualy) options, better code, better security and so on.
You can have a plugin that was not updated in a year with a vulnerability that was already patched, in that case you leave yourself open to attacks.
Its up to you to decide what is the best approach to updated.
I disable every update and do regular checks once a week.
The number of calls I have about update problems are far lower now than when the updated were automated.