This should not be a problem unless you enter your home country with a foreign passport or attempt to enter a country with which you have a visa valid on your home passport. I have dual citizenship and regularly travel on both passports as do many people who have dual citizenship through birth. Grenada citizenship unlike some of its counterparts does not distinguish between economic and birthright citizenship.
Should Grenada passport holders have any concerns about visiting countries that aren't easily accessible with their native country’s passport?
I am interested in Grenada's citizenship-by-investment program, which would allow visa-free access to China, Russia, Brazil and other places that would require visas if I were using my native country’s passport. For instance, would customs officials be suspicious of a U.S.-born passport holder going to Russia, etc., using a Grenada passport instead of his American one?