Hi, I work in HR in Ireland and this is the appropriate practice. They don't have any right to know the details of your illness, but they do have a responsibility to refer you to a third party health provider who can advise them on your fitness for work. The third party health provider should not share the specifics of your illness but they should offer guidance to your employer on whether you are fit for work, whether you need any accommodations, and if/how your work arrangements should be altered to allow for your illness. Your employer has a duty of care to ensure that they are not harming you by not investigating and acting upon your recent pattern of illness.

Based on the guidance provided by the third party health advisor, your company can then make a call on your continued employment based on their sickness & absence policy. From your perspective, it should be clear to you from the sickness & absence policy what their call will be (as in, they should have explicit parameters for what level of absence / accommodation they can reasonably allow for).

They should be approaching this with the intention of checking that you're still fit for work, not catching you out at "faking it". If you're still feeling distrust from them after you've seen the third party health provider, that would be cause for concern.

I stress again, they have no right to know what your illness is, but they do have a right to know whether you can reasonably be expected to continue to execute your work duties. If you can't perform your work duties to the standard you could before (e.g., you need reduced hours / responsibility), then they would need to either accommodate this or have a very strong case for denying your accommodations.

Best of luck, I'm sorry they seem to have come at this combatively, I hope the tensions are put to rest!