Remember that you can only be in either Police or Poseidon (can't be in both at the same time) while you can join the NHS even if you're in another faction
I imagine you probably are having issues originally connecting and aren’t really thinking about factions at the moment. When you are on the slot selection screen make sure you choose a slot in the purple section. The purple section is civilian and you do not need to be whitelisted to join that. All other slots require whitelisting.