For further clarification on this.
Do Rogues still get an extra skill only if Rogue is taken at the beginning (1st character level)? So maybe Rogue 1 -> War Cleric 1 -> Rogue 10...? I know it's only 1 skill but, if there's no real downsides...
Yes. Rogues will get their extra skill irregardless of when you take the level.
The only difference between War Cleric > Rogue and Rogue > War Cleric would be your initial options for skill points (Cleric can only pick from History, Insight, Medicine, Persuasion or Religion while Rogue can pick from Acrobatics, Athletics, Deception, Insight, Intimidation, Investigation, Perception, Performance, Persuasion, Sleight of Hand and Stealth) and your save proficiency (Cleric is proficient in Charisma and Wisdom saves while Rogue is proficient in Dexterity and Intelligence saves).
Either way, the bonus skill point can be put into any of the skill options for either class.
