Not entirely sure which component is at fault here, though I'm lead to believe it's GTM since enabling GTM adversely affect two other components and disabling it fixed the problem.
Two separate problems:
1) While GTM was enabled on my site, the Ajax Event Calendar plugin stopped functioning and would display a blank page whenever the shortcode was invoked.
2) I'm using a Suffusion child theme, though I'm not sure if this problem is related to Suffusion. Essentially whenever I clicked on the GTM tab in BP I would get a blank page - not a 404 error, just a themed empty wordpress page.
Since disabling GTM fixed both these problems, I'm not really sure what else the problem could be. This seems like a fantastic plugin and I'm really looking forward to using it. Any help would be greatly appreciated.