My contention is that while bigotry is undesirable, contemporary reactions to bigotry are disproportionate to its potential harm. See
here,
here and
here.
The examples that MrWookie provides of the costs of bigotry are mostly examples of bigotry
backed up by coercion. Some would argue that trying to prevent bigotry would help stop these harmful actions, but it would be equally legitimate to claim that trying to prevent coercion would as well. Additionally, attempting to prevent coercion could help those coerced in non-bigoted ways.
You could argue that targeting the roots of a problem may have other positive results and/or be more cost-effective. I would not be surprised if this were true. But at the moment, arguments I've seen along these lines seem very speculative and unscientific (if they don't just simply assert that Bigotry Is Wrong And Therefore We Should Do Something About It). I could certainly envisage a scenario where it would not be true (e.g. if it is very hard to get people to change their beliefs/have their children believe something different, or if the criminal justice system is very effective). Also, some statements of bigotry might be very unlikely to eventually result in harm.
Thus, I suspect that voicing/acting in opposition to bigotry, like many ostensibly charitable actions, is not so much about its actual consequences, but signaling to others that you share their values in order to reap the benefits of in-group solidarity.