Against a 4 man group, I'm not sure what to tell you but I did find blast shield to be rather helpful against a 2 man group. That and staying back what I could. Generally I was able to drop at least one of them and sometimes both but you need a gun that will kill quickly. Also as someone else said, packing an IED also helps if you can get it behind them.
Ha. You ran across a team that was organized - annoying indeed, but organized. Best bet is to not play them and move on, or have your team try a similar strategy - fight fire with fire. Most people hate when they come across teams like this, but it's actually pretty fun. Very competitive and nerve-racking. Just forget about it being win or lose and have fun with it. Set a goal of defeating them by creating overcoming strategies. Once you do win, you get a great sense of accomplishment. And don't talk smack to them once you do win, congratulate them on being so competitive and hard to defeat and ask for a re-match.
I've yet to see a shield/c4 team specifically, but I absolutely agree with your observation about these "annoying" team strategies can be fun to play against -- uually I find them to be a nice changeup in gameplay. E.g., a team of campers -- finding their flaw, converging on their camp spot from multiple angles as a team, etc, instead of just running around the maps looking for badguys like usual.
Already played a team of 4 doing this myself, probably my first few games of s&d. Personally, I have no problem saying it deserves a nerf, just like IED. It all is a bunch of tools used mainly by players with no gun skill who sit stationary. I'm not a huge player of MLG gametypes, but you'll notice it isn't included there. Why? Because it really has a lower threshold of skill than using guns. Whenever the solution to a strategy involves a "well you should've made one specific class with like 1 specific perk or done that thing first" type of response it is blatantly obvious that skill has gone out the window. Skill is at least somewhat transferable between guns, gametypes, and maps. How well does this riot shield tactic work in any game mode with respawns? Not nearly as well I am certain. Greater skill should always be connected to the winning team. Yet it isn't so in this case, so why pretend?
Additionally, I'll mention that this is the same exact kind of responses kids used to say in MW2 when a whole team decided to use scavenger or OMA and noob tube. Everyone knows that was terrible, and you don't see that combination still nearly as effective in titles made since then. The skill cap in call of duty should always be tied to player movement and gun skill as closely as possible. Force people to aim a gun and place shots correctly, get rid of things which undermine that.
Weren't you one of the ones who told people to adapt to the Worm? I mean it's no different then what these people are doing only the people who were using the Worm had infinite explosives and tacticals and had guns and they weren't exposed as much. Here's what I do when I encounter them I use a rocket with danger close and shoot it behind them they get so mad after I throw my C4 at them if they were using Blast Shield. lol They are easy targets because they are too slow to run away just find out what works against them the Riot Shields and C4s are fine. If anything this tactic is easier then Black Ops 2 because the fact they don't have infinite C4s or anything like that for that matter.
Stay at long range with LMGs and surround them. Cut them down collect the tags. LMGs give those shield users no room to maneuver because of the constant shower of bullets and almost no damage drop off.
This is very annoying. I am an avid S&D player and this is an outrage! I sometimes play bare bones with a knife in Search , its a fun alternative to run and gun, just to be killed half way out of spawn by a C4 because they have strong arm perk, Extra Lethal and C4 not to mention Amplify and takedown. Yes, it is somewhat easy to out smart them but still they can throw faster than people have time to react!