I use my iPhone X regularly at contactless terminals at stores and on the bus. The trick is to double click the lock button first, select a card if you want, then hold it by the reader.
I don’t have any problems with FaceID — it’s more reliable and easier than TouchID for me. I live in a rainy place, though. Obviously a YMMV situation.
With TouchID do you just put your finger on the home button and hold it by the reader?