To Topgoon,
I'm not completely against it, but it's new mechanic to 5E that will need to be considered across the board (I assume if we are letting resistances stack, it needs to be across the board and not a Ranger exclusive). Do only permanent resistances stack this way? What happens when there's 3 sources? Another side-effect that will be hard to calculate isn't in the damage reduction, but what this helps you avoid when certain spells/abilities that do more than just damage. Very similar to the Poison Resistance vs. Poison Condition situation I outlined above.
1varangian was only talking about giving a saving throw bonus instead of a resistance - since the saving throw bonus would compliment and add to the resistance. They werne't talking about stacking multiple resistances.
For the other bits:
5e design is more careful than you think about its style for allowing overlaps and double-ups.
For Dragonborn/dragon sorceress, it's like I said; you get a damage resistance from your race. You don't get it from your class, and you only get it from your subclass at a later level (level 6). In the case of dragon sorcs, the damage resistance is one part of the level 6 perk – and the lesser part at that. The perk at 6 lets you add your Cha modifier to all your element spells, which is a beefy perk since it's always-on. The ability to spend sorcery points for temporary resistance is negligible... It's not really a conflict as the value lost in overlap is nigh insignificant: the resistance you can gain comes only when you cast a spell of your ancestry element, and the the odds of you casting fire spells at something that's going to be dealing you repeated fire damage for the next hour is minuscule, in practice.
The other features of dragon sorc and dragonborn all compliment each other without any further overlap.
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Celestial Warlock and Aasimar have a double up on both gaining the light cantrip. It's not a big overlap. Again, the resistance base comes from your race. The subclass gets one of those resistances as only one part part of their 6th level perk, the more potent part of which is adding their modifier to all of their radiant and fire spells.
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Fire Genasi, again, fire resistance from your race... your subclass grants a fire resistance as one part of (once again) the 6th level perk. The more important part of that 6th level perk is the granting of a flying speed.
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Triton and fathomless is a repeat of the same: you get cold resistance from the race at 1st level, but the subclass only gives its double up resistance as one part of another perk, and only at a later level (once again, 6th). The other half of that 6th level perk lets you communicate both ways with any creature underwater, even if they wouldn't normally share your language or understand you.
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Giving flat fire resistance as an entire first level perk is a very clear misstep made by someone who is not well versed in the system and style of design, and doesn't understand properly how things are made to fit together.