Sorry to see you join the group @Katie46 - feel free to fill us in on your diagnosis/surgery/treatment up til now to get a 'fuller picture' of your story so far. ;)
I didn't do chemo or take those tablets - but I reckon, with a bit of practise, You should be able to just 'pop' the foil on the blister pack and drop the tablet from the pack directly onto your tongue? They may just be taking precautions in case the protective coating 'breaks down' if someone has washed their hands & 'melts' the coating & the active ingredient then comes in contact with your flesh? (I am just guessing, really! ;) )
Or you could just drop it onto a tissue & pop it into your mouth?
Maybe also ask your Onc and/or chemo nurses (or Breast Care Nurse) about it! Sounds pretty extreme to me!
Info from others (who've taken it) is here .... you may be able to glean some info from them?)https://onlinenetwork.bcna.org.au/search?domain=all_content&query=Abemaciclib&sort=-dateInserted&scope=site&source=community
take care & all the best xx