I can't believe that with mental health awareness and inclusivity being such a hot topic in current affairs, in 2023 that you cannot be aware that there is a very marked difference between the very common feeling of 'discomfort and awkwardness' (and even anxiety) and a set of physiological symptoms that manifest themselves as a result of a disorder and can impact peoples daily lives as you have described very detailedly in your OP that it interferes with her daily life, to the degree that it could be classed as a disability under the Equalities Act 2010.
Anxiety disorder is not the same as experiencing temporary anxiety. It impacts your heart rate, sleep, cognition, irregular heartbeats, chest pains, extreme perspiration, dizziness, nausea, stomach problems and/or diarrhea, respiration, numbness/tingling/pins and needles, tiredness, headaches, and of course, this is just common symptoms before you reach a panic attack.
Anxiety is not just feeling worried and a bit panicky. I can absolutely guarantee you if your suffered from it, you would not be 'unbothered' by it - your physiology, including the involuntary release of hormones designed to force you into feeling extremely bothered physically and mentally, would make sure of it.
As such, it's a good thing your employer has made, what seems very obvious to be the case, a reasonable adjustment for her. It could possibly be discriminatory if she does not progress in her career as a direct result of this disability unless it was absolutely necessary that she take part (which at 4 times a year, seems it's not). Justifiable discrimination isn't an easy cause to prove.
You might want to educate yourself a bit, and whilst you're at, be careful. Some equality training might be helpful for you.
As someone whom has been on the receiving end, I can tell you that 'because other staff don't like it' isn't justifiable discrimination, and can land people in court.