Can you be 100% secure in the validity of your beliefs, but also become upset when someone challenges that validity? I think not.
I don't think you can.
Here's my reasoning behind the above statement;
I can understand that it must be annoying and even hurtful to have your beliefs put down as nonsense or silly etc...
However, if you are truly secure in your faith, nothing anyone can say should really upset you as you know what you believe to be right.
Surely a problem only arises when what someone says triggers doubt within yourself, it is the anger and confusion from within yourself that upsets you, not anothers ignorant viewpoint.
Yeah, a whole bunch of thoughts, now that you ask.
Speaking strictly for myself, I don't find it at all upsetting when someone challenges my beliefs. If it's a fellow-Christian who's challenging them, I feel confident that I can find Biblical evidence to support them in about 99% of the cases. Biblical "evidence," of course, doesn't "prove" anything, since the scriptures can be interpreted in so many different ways. But when someone puts down my beliefs as being "un-Biblical," it doesn't bother me in the slightest. I know they're as "Biblical" as the next guy's. I'll even use your question as an opportunity to invite any non-LDS Christian to debate me one-on-one on any topic of general interest and conern to the entire Christian community. Any takers?
Again, this is only my opinion, but I believe it's probably shared by other members of my faith: The "anger and confusion" arises not not from doubt but from the frustration that comes when people misrepresent my beliefs. When somebody says, "Mormons believe [such and such]" and it's not true, that's frustrating. When we reply with, "No, that's not what we believe. We believe [such and such]," it would be nice to get an answer like, "Okay, thanks." Most of the time, though, that's not what happens and we get told over and over again what we supposedly
believe and teach.
It's frustrating to me to debate an atheist, because faith is something you can't explain in terms that's going to satisfy someone who doesn't believe. Most of the time, I shy away from debating atheists because it just seems to be counter-productive. I can respect an atheist's lack of belief, but I'm the kind of person who likes to find resolution in a difference of opinion, and a believer just can't hope to do that in debating with a non-believer.