My solution is simple: To tell the extremist elements that they can't dominate our discourse, and to meet both threats and any attempts to follow through on those threats with all the force necessary to dissuade them. The "nice" answer is wrong and has all sorts of "not nice" results. And however hard this may be to believe or accept, the potential losses of knuckling under to terrorism are unbounded. Because the thing is, it's not about the grievance they say it's about. There's an infinite supply of grievances, and even if there wasn't, if you leave the decision about whether you've discharged the grievance in the hands of the terrorist they can always decide you haven't done enough. What it is about is that they can get more benefit from the terrorism than it costs them. That is what you must be concerned about, ensuring that the costs of terrorism exceed the benefits, and one easy (and arguably necessary-but-not-sufficient) way to do that is to make sure they don't get benefits. Official "Draw Mohammed" day is a good solution on the side, by raising the costs of terrorism.
Any policy that has the end result of moving the cost/benefit advantage of terrorism in the direction of "benefit" is wrong, especially any that cross from net-negative to net-positive. Regardless of how "nice" it is. Regardless of how well-cloaked in moralistic bibble-babble it is. And it will be so cloaked; the ability of humans to rationalize the short-term convenient answer is nearly unbounded. This is part of the basic contract of civilization and operates at a lower, more fundamental level than most people are used to debating at, in that if terrorists are allowed to tear apart civilization (the ultimate end result if this policy of appeasement is followed), most of the rest of our debates are rendered moot. The first order of business is make sure we still have a civilization in which to have our arguments about what it should be.
I've gone down to this level because it's really important. The US remains a ways away from this being a serious problem, but I am concerned about the number of draws we're making against this account without depositing things; we're a ways from bankrupt here but the trend is strongly negative lately.
I have carefully referred to "nice" policies rather than naming names, but in most cases there are, shall we say, correlations between political parties and the "niceness" of their policies; applying this discussion to their country's policies is left as an exercise for the reader. But there is definitely a time and a place for "not nice" policies, if you actually want your civilization to survive.