Well thats incorrect a class will always get their special feats, such as Danger Sense for Barbarian level 2.
Whats not multiclassed is proficiencies. For example you wont get heavy armor from Fighter or Paladin if you dont start as them. You will only get Medium armor if you multiclass to them.
But you WILL get heavy armor from Ranger, assuming you pick the special option, because then its not a class proficiency, but depends upon your explicitly picking a feature that grants it to you.
Likewise if you multiclass to Cleric the Life and Nature Domains will always give you heavy armor; and Tempest and War will always give you heavy armor and martial weapons.
You also will always only get one Major Save (Wisdom, Constitution, or Dexterity) and one Minor Save (Strength, Intelligence or Charisma) from the first class you pick. Multiclassing further wont change this. You have to either get feats or class features (example: highlevel Gloomstalker IIRC gets Wis and Int saves).
Danger Sense should thus work, and if it doesnt, it needs to be fixed.