Your beard is excellent. And in no way you look like a terrorist, don't bring yourself down for this.
That's corporate bullc**p I tell you... how many times it happened to me. And I've got a dark brown-black beard and I heard this kind of thing countless times from coworkers to "friends" to relatives.
You look really good with your beard, you might get a different haircut or maybe a LITTLE trim on the beard ONLY if it's absolutely necessary, but really, don't do it because other tell you to do so.
Show that you're an awesome person and you'll earn their respect and they will eventually get over it. It's how I did, for now...

I'm unemployed again and it will be a pain to go through the next job appointments with the beard again!