SOLVED!
I found the right version of Logicity that is compatible with the Sage 100 2016 CR runtime. Now both work.
Below are the detailed notes if you're interested:
Whenever you install another application that uses the Crystal Report Runtime engine, you have to be careful of conflicts with the Sage version of CR Runtime.
As of July, 2018:
Sage 100 2016 uses Crystal 2011, runtime SP 13
Sage 100 2018 uses Crystal 2016 runtime SP 21.
https://support.na.sage.com/selfservice/viewContent.do?externalId=50666&sliceId=1
Logicity v 1.8008 uses CR runtime 13 (1.8009 patched up to a higher CR runtime)
Logicity v 1.9 uses CR runtime 21
https://www.logicitysuite.com/version-change-log.html
The trick is to install a version of Logicity compatible with Sage 100
https://www.logicitysuite.com/downloads.html
By default, Logicity will install another instance of SAP Crystal Runtime that shows in Control Panel / Programs and Features. The Sage 100 crystal runtime does not show in Programs and Features.
However, you have the option of not installing the CR runtime with Logicity. It's already there for Sage, so you don't need another instance.
I also recommend unchecking the checkbox to associate .rpt files with Logicity