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The regulations are indeed lessened depending on the object, and for return missions from objects like the one targeted during the Hayabusa 2 mission it would appear the samples can have an unrestricted return. Thus, no quarantine is required for the purposes of protecting earth (though they might do things to protect the samples from earth).

From the original Hayabusa example it would seem that while preventing planetary contamination is obviously desirable, science can still be done on heavily contaminated samples (only about 0.1% of the returned sample was actually from the asteroid).

Going back to the question in the OP, here's a source that overviewed the plans for the Hayabusa 2 mission, which was classified as a Catagory V unrestricted return.

Page 34 of the PDF has a flowchart used for determining such catagorization and comes to the conclusion that

So for asteroids of similar type to the one targeted for Hayabusa 2, it would seem planetary protection procedures like quarantine would not be required.

The regulations are indeed lessened depending on the object, and for return missions from objects like the one targeted during the Hayabusa 2 mission (C-type asteroid) it would appear the samples can have an unrestricted return. Thus, no quarantine is required for the purposes of protecting earth (though they might do things to protect the samples from earth).

However, it depends on the type of asteroid. P and D type asteroids are classified under the same classification as something like Europa, and have strict requirements for handling. I believe this is mainly due to the limited data on P and D type, leading to a "better safe than sorry" approach. (This might have changed in recent years, my source is about 10 years old).

From the original Hayabusa example it would seem that while preventing planetary contamination is obviously desirable, science can still be done on heavily contaminated samples (only about 0.1% of the returned sample was actually from the asteroid).

Going back to the question in the OP, here's a source that overviewed the plans for the Hayabusa 2 mission, which was classified as a Category V unrestricted return.

Page 34 of the PDF has a flowchart used for determining such categorization and comes to the conclusion that

So for C-Type asteroids, it would seem planetary protection procedures like quarantine would not be required.

From the original Hayabusa example it would seem that while preventing planetary contamination is obviously desirable, science can still be done on heavily contaminated samples (only about 0.1% of the returned sample was actually from the asteroid).

Finally, here's a source that overviewed the quarantine plans for the Hayabusa 2 mission, which was classified as a Catagory V unrestricted return.

I would assume that asteroids are abiotic so the regulations would be lessened, but would planetary quarantine still take effect in mining procedures?

The regulations are indeed lessened depending on the object, and for return missions from objects like the one targeted during the Hayabusa 2 mission it would appear the samples can have an unrestricted return. Thus, no quarantine is required for the purposes of protecting earth (though they might do things to protect the samples from earth).

From the original Hayabusa example it would seem that while preventing planetary contamination is obviously desirable, science can still be done on heavily contaminated samples (only about 0.1% of the returned sample was actually from the asteroid).

Going back to the question in the OP, here's a source that overviewed the plans for the Hayabusa 2 mission, which was classified as a Catagory V unrestricted return.

https://science.nasa.gov/science-pink/s3fs-public/atoms/files/Hayabusa-2_--_Hajime_Yano.pdf

Finally, here's a source that overviewed the quarantine plans for the Hayabusa 2 mission, which seems to have similar requirements as the Hayabusa 1 mission.

https://science.nasa.gov/science-pink/s3fs-public/atoms/files/Hayabusa-2_--_Hajime_Yano.pdf

For unsterilized samples returned to Earth, a program of life detection and biohazard testing, or a proven sterilization process, shall be undertaken as an absolute precondition for the controlled distribution of any portion of the sample. A quarantine facilities are required and corresponding procedures for sample handling to be developed.

I would assume that until asteroid mining becomes a regular thing, similar procedures would be followed.

Finally, here's a source that overviewed the quarantine plans for the Hayabusa 2 mission, which was classified as a Catagory V unrestricted return.

According to the most recent scientific knowledge combined, the Hayabusa-2 team considers the 1999 JU3 mission as Category-2 for the outbound and Category-5 “unrestricted” Earth return for the inbound.

Page 34 of the PDF has a flowchart used for determining such catagorization and comes to the conclusion that

No Special Containment Required Beyond What Is Needed for Scientific Purposes = “Unrestricted Earth Return”

Wikipedia has an overview on what these categories indicate:

https://en.wikipedia.org/wiki/Planetary_protection#Target_categories

Category V, Unrestricted Category V: “Earth-return missions from bodies deemed by scientific opinion to have no indigenous life forms.”

So for asteroids of similar type to the one targeted for Hayabusa 2, it would seem planetary protection procedures like quarantine would not be required.