Responding to this here:
I-Red is perhaps the largest and most well known Caldari RP group out there right now. This is their recruitment thread on forums.
[I-RED] Ishukone-Raata Employment Services - Corporations & Alliances / Recruitment Center - EVE Online Forums
LUMEN also has a contingent of Caldari rpers (either mercs or representatives from State groups). That often makes for interesting internal tensions/roleplay betweem them and the Amarr members. Recruitment thread on forums:
Societas Imperialis Sceptri Coronaeque (SFRIM) - Amarr Loyalist, PVP, PVE & More! - Corporations & Alliances / Recruitment Center - EVE Online Forums
There are other smaller state focused groups or solo roleplayers who can be met in “The Summit” in game or on the Roleplay Discord Roleplay is Primary