Final answer:
The claim that all Latinos share the Spanish language as a common ethnic characteristic is false, given the diversity within Hispanic communities and the presence of other languages among Latinos.
Step-by-step explanation:
The statement that one common ethnic characteristic shared by all Latinos is the Spanish language is false. While the Spanish language is a significant factor used by the U.S. government to categorize people into Hispanic or not Hispanic, the term 'Hispanic' encompasses a diverse range of subgroups and nationalities. Consequently, not all Latinos necessarily share Spanish as their language, since there can be variations, such as Portuguese in Brazil or indigenous languages across Latin America. Moreover, people of any race can be Hispanic, further illustrating the diversity within Latino ethnicities.