Your guy at Autozone is an IDIOT! You can switch back after you put synthetic oil in, I don't know why you would, but you can. There is no special filter for synthetic oil.
There is so much misinformation regarding synthetic oils. There are numerous papers available online etc regarding synthetics. Check with ASE, Mobil, RedLine, Amsoil, BMW, GM etc etc. The vast majority of auto manufacturers utilize synthetic solely. Far superior protection, longevity, resistance to breakdown, less apt to failure under high heat situations, and more.
I would definitely use synthetic, with a Mahle or Wix filter.
Just my 2 cents. Your milage may vary. Limited to stock on hand. One coupon per customer. Not to be used in conjunction with any other offers. This is offer may expire at any time. Dealer to retain any rebates or incentives.