Hit 'em Where it Hurts
When raging, they have resistance to bludgeoning, piercing, and slashing damage. Uncanny dodge is a reaction. With those two things in mind:
- Use elemental damage attacks. If they're hit with fire bolt rage won't protect them
- Gang-up! Since uncanny dodge is a reaction, you can only use it once per combat round. Multiple attackers means they have to choose which to dodge.
- Use hidden enemies. Uncanny dodge only works against attacks you can see. Hidden attackers are not seen, and can't be dodged.
- Tempt them with opportunity attacks. Both OAs and uncanny dodge are reactions, so tempt them to use their reaction on an OA to get in their sneak attack damage a second time that round (you can sneak attack once per turn)
- Multiple combats. Rogues are Dex-based, and thus get very little out of multiple levels of barbarian. Therefore, their number of rages are going to be limited. More combats means they have to choose when to rage and when not.
But Not All the Time
While the above points can counter the barbarian/rogue's abilities, don't do it all the time. They took those abilities because they want to be that awesome. Be a fan of the player and let them be awesome. For every few combats where you shut down their abilities, give them one where they shine!
If the player is constantly unable to use their class features, it starts to seem like a waste, "why did I get uncanny dodge if I can't dodge anything?"
As the DM, it is your job to make an exciting and fun story for the players—including yourself. Don't shut down one player all the time, or it'll be less fun for them.
I Don't See a Balance Concern
While it seems like an overpowered combo, it's not. Rogues are Dex-based, and most of the barbarian features focus on Str-based attacks and thus the two classes don't play well together for more than just a small dip (a level or two).
While it's an interesting trick, it's nothing game-breaking.
Your Specific Concerns
It could trivialize boss encounters, or put them in a place where they're safe in boss fights
If you only have boss encounters, this is an issue. But as long as you sprinkle in non-boss encounters it should be good.
Compared to the rest of the party, this character would have the best defense, even naked
Not quite. One half-damage reaction per round and resistance to weapon attacks may make your HP go a bit farther, but a rogue/monk will have a higher AC when naked than a rogue/barbarian. As above, hit 'em where it hurts to get around the halving of damage.
You can get more defense by taking Bear Totem Barbarian (resistance to all but psychic), and Evasion (at most half damage to all saving throw damage spells), which makes the difference in "naked" defense capability worse
As I mentioned above, going deep multiclass rogue/barbarian is going to have a lot of "dead" levels since rogue is Dex-based and barbarian is Str-based. Many barbarian features require Str checks/attacks and rogue features proc off of Dex checks/attacks. This makes the non-defense features mutually exclusive.
Assuming a rogue 5/barbarian 5, here's what you get as a barbarian that is of little use:
- Rage bonus damage (only applies to Str-based attacks)
- Unarmored defense (Con will need to be 14+ to be better than armour, and won't likely be that high due to 13 Str requirement for multiclass barbarian)
- Reckless attack (requires Str attacks)
The following features will be useful:
- Rage resistance
- Danger sense, ironically, is surprisingly useful even for a rogue with high Dex and proficiency in Dex saves
- Bear totem resistance
Extra attacks is of dubious use, considering that you can only add sneak attack damage once on your turn, and most of your attacks will be with advantage, and thus are super-accurate to begin with.
For all those things, you're giving up 5 entire levels of rogue, which include evasion (better than danger sense), two ASIs, an archetype feature, and 2d6 of sneak attack damage.
Multiclassing barbarian is a decent way to improve your defenses, but you sacrifice some potent rogue features to do so.