$300 * 12 (months) = $3600 (yearly food budget) * 0.06 (rewards) = $216 - $95 (annual fee) = $121 reward dollars annually.
Now consider the amex interchange rate of 1.95% + $0.10 per retail transaction. Let's say I shop 24 times in a year. ($0.10 * 24) + ($3600 * 0.0195) = $72.6.
The most amex could possibly lose on my card in a year is $73. But only the most disciplined people will use it for groceries and only groceries.
One thing that should be made clear is that the cash back is not on groceries, it's on purchases made at grocery stores. Groceries bought at Wal Mart, Costco, Target, etc. don't qualify. Similarly, the percentage cashback for gas doesn't apply to gas stations attached to other stores, e.g. Murphy, Kroger, etc.
I suppose this card could be different, if so it might be worth the annual fee.
If you spend $263.89 or more per month at grocery stores it makes sense to upgrade to the Blue Cash Preferred. Keep in mind this excludes Costco, Walmart, Target.
If you buy groceries at Whole Foods and are a Prime member, you can get 5% via the no annual fee Prime Rewards Visa, which makes sense if you spend under $95/(0.06-0.05)=$9,500 per year at Whole Foods.
Bonus, the card is clear plastic which everyone comments on when they see it.