I've seen this term banded around quite a lot lately, and generally not portrayed in a pleasant manner either, so thought it's well overdue time to address it.
Firstly, I'll state that all player types can add value to a game, so this is no criticism of players who don't have interest in passive community gamplay.
There are many core player types that make up an MMO RPG. The term "care bear" is usually aimed at players who prefer to play as part of a friendly community. The focus is usually around building or character development, and quite often has little tolerance for "trolling or griefing". Usually there may be less emphasis on progression, but the sense of respect for other characters and property plays a stronger role.
What does this player type add to an RPG?
Firstly, a sense of community. For some players, community is of little interest. You go into a town to buy your supplies, but what is the glue that holds the people of that town together and supporting each other rather than fighting among themselves? The mindset usually leads to group players, picking complimentary skills and working together. This increases the opportunities to join parties and establish longer term friendships in game. Usually these player types don't much care about being seen as "the best" at what they do, or owning the finest of equipment, but most aim at least to see a sense of progression and a gradual improvement in their quality of "life" as a reward for their efforts.
In many games, including WoW, it was this wide base of the community that kept players coming back. In recent years, where games have targetted rewards purely at the higher end of more capable players and pushed up difficulty too far, it's presented a barrier to their progression. Combined with the pressured environment and stress at the higher end, it's led to many of these community "pins" falling out, and communities gradually falling apart. I've seen it happen more than once.
Interaction with "thieves" and other threats
Thankfully, the justice system within the game allows for player-driven resolution of some threats. Minor incidents will largely be shrugged off by the player base, though repeat occurences or trolling will be seen as far more damaging. This carried the threat of driving away these core players, and the cascade effect may then follow. As such, there will likely be a heavy reliance on the justice system and investigation.
Thieves for example, are often seen as freeloaders who can't be be bothered to put in hard work, but are happy to undermine the enjoyment for other players by taking their rewards.
As long as there is the perception of eventual "justice", and the degree of loss isn't too great, the appeal isn't likely to suffer too greatly.
Game growth and stability
Most MMOs rely on good numbers of players with a varied mindset to succeed. This would appear to be the case with Elyria too. Here, players need to provide food, equipment, clothing, build and more. Combat is a small proportion of the career base as a result. Any army in Elyria has to be well supplied to succeed.
As a result, the appeal for the would-be farmers and other crafters and gatherers has to remain. If the mindset adjusts so that theft is commonplace for example, and little that is earnt is kept securely without loss, the view will increasingly become that there is no point in trying. At that stage, the model collapses, and the armies die off too. A waste at the very least.
Summary
In short, "care bears" are a significant and key part of the player community. If you don't fit into that category, they will still most likely be a core part of the player base that you rely on to keep yourself functioning well. Work with such players, not against them, or it will likely be to your own detriment, and the detriment of the game's longer term success.
Trolling and griefing and never funny, and never popular, usually nothing more than an indication of the griefer's own lack of social skills, maturity or empathy.
Rest assured that many of us will be looking out for those of you that classify as "care bears", and aiming to make the game as friendly and as fair a place as we are able. If we can offer rewards, hire mercenaries and work to stamp very heavily on crime through the court system, rest assured that many of us will.
If you're considering Elyria, but are holding back as you're concerned about it falling apart, don't. Simply speak to a few of the nobility who are looking out for the common people, and we'll take care of you as best we can.