Good grief.
Appeasement? Exactly how have we/Obama been doing that? Ridiculous.
Terrorists hope like hell that we will blame "Islam". If you want to play directly into their hands and contribute to the escalation of indiscriminate violence, just blame "Islam" and "Muslims" and "go after" them, isolate them, oppress them, kill them.
If you want to know who to listen to, do NOT listen to any fool that tries to suggest that the problem of Islamic terrorism is simple and all we have to do is "get tough" with Islam.
I'm pretty sure that "Islamic" terrorism is heterogeneous, being a varied conglomeration of political, cultural, economical, ethnic, and religious influences. It should be possible to "go after" actual terrorists and at the same time seek to understand and mitigate (as able) the various influences that give rise to its occurrence and growth. Part of this is to distinguish and encourage the idea, as able, that good/right Islam is by definition that which does not condone terrorism. And to partner with those that support this notion.
To strive to do this is not appeasement. Even if you think it is. !