I have solved the restaurant issue by always paying cash in restaurants and bars. The folks like the cash tips too.
Diesel stations are the worst as many that take the cards directly at the pump for gas, do not have readers on the diesel pumps.
I "pre-pay" for the gallons the driver information canter says I burned since the last fill up. If they insist (some smaller private stations) on keeping the card anyway, my DW stays there and keeps an eyeball on the card.
This double swipe scam took me by complete surprise as she was a very smooth operator (and cute as I recall).
From what I have read about how the RFID "chip" works, removing it will soon not be an option as merchants convert to the newer secure scanners that require it to buy from them. This insures that the "white credit/debit card scam will not ever work again as only YOUR card will work the scanner.
Which Credit Cards Have RFID? | LowCards.com
There are VERY simple prevention methods for securing your chip without destroying your credit card.
Credit Card Protection Sleeve | Identity Stronghold
For 2 bucks ($9.99 for 5) you just slide the card in a sleeve and you are safe.
As to not signing the back (an X is ok (I guess) as long as it is your actual signature), in many government offices, the card will be declined (like the post office). Signing it is actually more secure than not, because an alert cashier will compare the signature on the scanner (shows up on her screen) to the back of the card.
"Ask for ID" is not acceptable at the post office either as I found out some years ago.