Thanks for saying that
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Interesting question. For myself, personally, I think I'd be ok with a professional carer irrespective of gender. Providing they had the right qualifications and recommendations - it would require thorough research to hire the right carer/find the right care home for myself or a family member.
I will say that, as a woman, I do have a slight preference for, say, a female doctor, particularly if the appointment is regarding intimate care.
For a family member, it would depend hugely on their own belief system to ensure their comfort. My mum, for example, I guess I would call GC so I would know and accept that she may not be comfortable with a trans woman administering care.