Hi,
You were misinformed by Modern Tribe, this isn’t a problem with any theme. As you said the problem persist with Twenty Twelve theme.
The result of our analysis indicates that you build this current site in a subdomain and at the end of it you moved everything to the main domain.
subdomain: http://2014.charleswoodunited.org/
domain: http://charleswoodunited.org/
You left the link of the calendar pointing to http://2014.charleswoodunited.org/calendar/ and when you hit the next month button is made an Ajax request to http://charleswoodunited.org/calendar/2014-04/
This is interpreted by the browser has a cross-domain Ajax request that is denied because of security reasons.
What is wrong here is just the Link of the Calendar menu item.
Instead of http://2014.charleswoodunited.org/calendar should be http://charleswoodunited.org/calendar
This will probably solve it.
Sorry for some technical words.
Best Regards,
Rui