If you're talking about feat multiclassing, then you don't really give up anything as long as you only power swap when it is reasonable and advantageous. In that case you can't really dilute your role much. Around 75% of characters I make have a multiclass to some degree. Currently, I play a Hexblade with Battle Awareness fighter MC (which lets me attack when adjacent enemies shift or attack someone else, and they always do), Quicksilver stance (which gives basic attacks as move actions), and Striking Resurgence feat (which lets me attack when I use second wind). So, despite MCing to a defender class, I'm just using it to get more attacks, i.e. striker effects. I'm more anti-defender than defender, since I force attacks away from me. I make a fair number of OAs, but not in a defenderish way - I'm just doing them to get more damage, not to stop someone or present a threat. Since I'm getting them from being invisible and stealthed, the enemy doesn't really even know they're threatened in that way.
Paragon Multiclass can cost you a lot (4 feats and a Paragon Path) and is rarely worth it. Possibly never worth it now that hybrids are around, although it's still possible to make a good character if you really know what you're doing. I've played with only one paragon MC, which was a Rogue/Wizard using an accurate frost dagger with frostcheese and rogue weapon talent for very high attack bonus. He basically acted like a wizard all the time at paragon levels, and was probably squishier than the average wizard, with a slight nod toward strikerness in that one guy in his burst took the Sneak Attack damage. So he definitely diluted his strikerness and pretty much fully converted to controller. But I'm not sure there was really any overall benefit to the build that he couldn't have just accomplished as a straight wizard.
For hybrids, I've played with a lot. I think most hybrids are actually multi-role hybrids, or the most effective hybrids anyway. When you have 2 of the same role, it's just awkward more than anything else. You have multiple powers that do the same thing, but can't be used together. Multi-role though, you can find some synergies and ways to use up your full complement of actions without interfering too much. We have 2 multi-role hybrids in our current group:
The Swordmage/Wizard is our only true defender... and yes, that role is very diluted. Swordmage hybrid can mark only one guy until that one dies. He has a really questionable amount of HP for a defender, but very high defenses all around. I think he would be a horrible main tank in most parties, but ours has a lot of offtanking and everyone is tough. That one dude he marks, though, is basically out of the fight. If he attacks the swordmage, he misses. If he attacks someone else, he gets his damage or attack cancelled. Then, the wizard half does his wizardy things. The one time we fought a solo solo, it was pathetic. It hit the swordmage maybe twice, and hit no one else, ever. It tried, but was countered every time, even multi-attacks and area attacks. The swordmage got bloodied from those 2 hits, though, but was promptly healed with one spell from...
The Sorcerer/Warlord, right after he used a reaction to get himself and me free attacks from the tank being bloodied. He has the high damage of a striker - possibly the best in the party (he has the best at will damage and the best nova damage, but I can sometimes do more through extra attacks and zones). And he can toss out some great leader buffs, heals, and extra attacks too. He really does well with either role, or both at the same time and is probably the most optimized character in the party. If there is anything missing from either role, it's well concealed. I have a strong streak of jealousy toward this character, although I know I can do some things better too.
