ISO 10993: Biocompatibility and Use of Textile Materials for Skin Contact Devices

General Questions:
I need help in understanding when testing is required?
How to establish material equivalency?
What constitutes a material with a demonstrable history of use in a specified role?

ISO 10993-1 clause 6 states in that the Selection of Biological Tests:
“Evaluation may include both a study of relevant experience and actual testing. Such an evaluation may result in the conclusion that no testing is needed if the material has a demonstrable history of use in a specified role that is equivalent to that of the device under design.”

Scenario:
Suppose I intend to design and manfacture a medical device that uses "everyday textile" materials (e.g. velcro, underwear elastic, bra-straps, metal buttons used in jeans). These materials will be used to attach the medical device to the patient skin. These attachment materials will make surface contact with the patient skin for <24h (not in contact with mucosal, or breached/comprimised skin). After assessing the device's intended use and having completed a material characterization with sufficient information to establish material equivalency...

Is it reasonable to justify that based on similar role in exposure to skin contact, "everyday textile" materials have an established history of use, and therefore no biocompatibility testing (such as sensitization, irritation and cyctotoxicity) is needed?

How to proceed depends on your regulatory context. Within FDA jurisdiction, you have someone to ask, and on the other hand, you'll be subject to judgements that may seem arbitrary. In Canada and Europe, the process is somewhat different.

Guessing that you mean FDA jurisdiction: The FDA does not provide a rule or guidance on how to make that judgement call, and the answer would be critical for you, so I'd not go by unqualified opinions (such as mine: based on your description, no testing is required) you might get here.

You could try asking DSMICA, but my experience with them over the past couple of years is that they tend to call you up and answer verbally so as not to create a record that can be cited.

You might need to follow the formal-interpretation route to get an answer you can actually hang your hat on.