ETA – Plenty of client companies would sack you off a job for using a hands free
Plenty of places put a lot of pressure on people to answer their phones wherever they are. Place I used to work used to ring me everyday at about the same time as I was driving into work even though they knew I would be driving in. I just used to let it ring in my pocket. I asked about a hands free, but it was a no-go.
it needs to be answered without physical interaction to be ‘hands free’ iirc.
I think that button press is permitted, but am not sure whether that applies to the phone or the handsfree kit. Most specific handsfree kits are one button to answer, so I assume this is legal.