Is there a good privacy focused app I can use to check my calendar and mute my phone if there is a meeting?

No need to install an additional app. That option is provided by the OS.

Settings > Notifications > Do Not Disturb > Schedules > Enable Event toggle

    treequell Thanks, I had not found that. It seems a bit too hidden away to be accessible and visibilble to tweak and have granular control. I was hoping there was perhaps a privacy version of Macrodroid.