At this time it is not possible to embed Google Calendars (or any other external calendars) into AChurchNearYou, and adding this functionality isn't on the current roadmap (www.achurchnearyou.com/roadmap)
At this time it is also not possible to import a feed from an external calendar into your AChurchNearYou calendar or take a feed from AChurchNearYou to import into an external calendar.
However, the project team are aware that these are functionality options in which churches are interested, and these are areas which are in discussion. In fact, following the recent Church of England Digital Labs Live (see: https://www.churchofengland.org/more/media-centre/stories-and-features/digital-labs-live-2019-mediacityuk), and with one of the two winning teams being ACNY Connect, keep an eye out for some very relevant options on their way soon.
AChurchNearYou receives around 10 million page views a year and many visitors are searching geographical areas looking for services and events near to where they are, or will be, on a particular day. Think of it a little like a comparison site; you'd rather the information was there in front of you than having to navigate off to multiple different websites to work out what suits you best.
Often members of the public use AChurchNearYou to browse lots of churches in an area to find suitable services, if the services are all on AChurchNearYou it makes it far more likely that someone will attend your church, whereas if they are sent off to a church's own site each time, that process becomes too convoluted.
The more information, services, events, and facilities a church posts to AChurchNearYou the higher the traffic they get, the more appropriate tags a church uses on services and events the more searches a church appears in the results of.
Churches cannot switch off the AChurchNearYou native calendar function on their profile.