Can anyone change the Church Profile information?

In Freemium, yes.  Once you have a certain number of followers on your app, it will require multiple people to approve changes to the Church Profile.  This is very similar to the flagging logic.  It is likely that 3 people will need to “Love” your change before it can take effect.  This too prevents people from changing the Church Profile without cause.  But it also provides the church with a Wikipedia style ability to get mistakes caught and updates posted more quickly.  In Premium, church leadership has the ability to reject or approve all updates to the Church Profile before they go live.