Maybe a better (somewhat ironic) comparison would be the classification of OTL English as a Germanic language—the extensive French influence on it has made it highly divergent but its core remains Germanic.
TTL Brythain would be Celtic but with such extensive Latin influence as to dramatically diverge it from the Celtic mainstream
EDIT: I’d also argue that a religious Schism wouldn’t necessarily have to take place to cause a rejection of Latin. Political tensions could be enough—have whoever rules Rome (or maybe Gaul?) demand tribute and vassalage and then even try to invade Britain. When this is repulsed it sets a precedent of bad blood between Britain and the Continent
TTL Brythain would be Celtic but with such extensive Latin influence as to dramatically diverge it from the Celtic mainstream
EDIT: I’d also argue that a religious Schism wouldn’t necessarily have to take place to cause a rejection of Latin. Political tensions could be enough—have whoever rules Rome (or maybe Gaul?) demand tribute and vassalage and then even try to invade Britain. When this is repulsed it sets a precedent of bad blood between Britain and the Continent