Just got back from Germany (Munich and Rhine). I have a chip and signature card and it only failed me once at the Frankfurt RMV machine. Worked in every other machine and place of purchase. Many banks will have a chip option now if you call and ask. I was using Chase Sapphire.
Also, every where I used my card (except for automatic machines for train tix etc) the machines that took the chip cards all had a place to swipe for magnet cards too, so you should be fine, especially for hotels and such. I also used the DB app so you can use this to by most of your regional train tix and not have to worry about the card type. (you will need to use the purchasing credit card as ID to show with the code on your phone if you use this option).
Also had no problem with my magnetic debit card for retrieving cash at ATMs in Germany.