I feel them. But they don't bother me. In fact, it can be very aggravating when I lose the feeling of clothes, because along with it I lose *all* proprioception/tactuile sensation for a while. This usually happens after a period of hard concentration, such as writing a test or doing my job (translation). During the concentration period I don't notice anything missing, but after that, when the update of the senses lag, it can be bad.
Feeling clothes continuously caused me to sort out my wardrobe and keep only cotton, flannel or jeans items. And I cut out tags. It helped me reduce irritability.
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"...unless you have a morbid fear of dying."