The shul I go to has a tradition to pause during Kiddush for people to say L’chaim. (during the day and at night. Before saying Borei Pri Hagafen.) I thought this was only permitted for Sephardim as it is considered an interruption for Ashkenazim. Or is it permitted because it is an outreach shul and there is a long tradition of doing it?

Since the ‘L’chaim’ blessing is said before the brocho is recited, there is no issue of Hefsek or interruption.