I think the best thing is to try and get her used to them but to do it gradually so that there are no traumatic or shocking incidents that set her back by reinforcing her fear. That said, while you want to avoid trauma you do not want to avoid anxiety and discomfort...she will unfortunately feel that initially as it is part of the process but will wear off, hopefully.
I would make a list of things like, start with you wearing a scarf like the seasalt handyband or a friendly looking mask just round your neck around the house, but with face showing. If you start with the handyband then the next stage is pulling it up onto your face a bit, then next stage try a mask round the neck for a while, then the mouth, then the nose. It may take several days of each stage for her to get used to each before you can move on. But there won't be any big steps like suddenly everyone in masks, each step will be small and once she is used to the rest.
You could get her involved in this, eg agreeing on what little thing she will try each day, but you will have to be firm that the steps have to be taken. Maybe she could pick little rewards for along the way.
You will also have to prepared to tolerate her anxiety long enough for her to find out that nothing bad happens, and people are jsut themselves but in masks. Explain to her that sometimes we can feel worried but if Mummy says it is all safe then she is ok to just let that worry and scared feeling be, and it will go away by itself after a while.
Other things you could try are just getting her used to the items, even cutting some up to make things, getting the toys involved. There could be a toy that is confident and one that is a bit nervous but agrees to try wearing one for a bit, when she gets to the stage of trying one on they could do that together for a bit.
Also could you pick out some fabrics you like that each family member has chosen to suit them, and always wear them specifically as in Mummy's mask etc. So that the mask is not just hiding someone's identity but expresses some of their identity...Mummy chose these nice flowers etc.
Sorry if none of this is any use...just brainstorming.