There is a setting in the Google Home app that will limit queries of your account to not include personal information e.g. not to list calendar entries when asked.
You can also set up multiple users voices so it will only answer from the account of the person asking (of enrolled)
The device still had full access to the account but chooses what to answer with.
To be honest to get the most out of the device you really have to commit to giving Google access to most of your life, it's a personal trade off.
Having said that it does make a nice voice controlled streaming radio (at least in the UK where it had full access to the complete BBC radio output)