The double pipes were widespread in ancient representations of musicians. 8 archeological figurines carved in stone playing double pipes have been found in Ibiza, Spain.   6 of these figures are female. (source) 

In European medieval manuscripts
it can be hard to tell if a man or a
woman is being depicted.

This hybrid is definitely part female
by the hairstyle (date c.1300).

1489 Frontino, Italy, alterpiece (detail)

1533 Design for a triumphal arch for Anne Boleyn's coronation procession in London, England.
Were there women pipe and tabor players at this time or was this just part of the design to look
dramatic and shocking.

A girl child modelled in France in 1760. The pipe is missing.

This is a curiosity (Wentworth Castle).
A 17th/18th century lady bare-breasted
and with her skirt wrapped
around to show off her shape.

The symbolism of the portrait is clear.
What does this say about the pipe and tabor?

In the 1929/1930's Joan Sharp (1898-1968) was playing pipe and tabor for morris and country dancing in England and on tour to the USA and Canada..

Joan Sharp and Douglas Kennedy

Some morris dancers were completely against women as dancers, managers and musicians until early 21st century. In April 1934, one dancer of the East Surrey Morris wrote a letter in which his criticism of the intervention of women in morris dancing was unequivocal: "As regards men’s morris, my feeling is that it should be entirely man-managed. Women should have nothing to do with its management at all." (source)

source

Despite attitudes such as these some women contributed fully to the morris movement. Winsome Bartlett in 1968 for example helped to set up, teach and play the pipe and tabor for Dartington Morris Men. She also made pipes and tabors, sang and appeared on the radio playing the pipe and tabor (1953).

1970 Winsome Bartlett playing for Dartington Morris Men

A Miss Barnett was praised by the Oxford University Morris Men:
" Our inspiration was Miss Barnett (Mrs Heffer) who was the Oxford teacher at that time and one of the few women really capable of teaching Morris.... the more observant and honest men admitted that on points of a pure technique practised women had an annoying habit of doing better than men."

France, 21st century.
There seems to be no
discrimination in Provence.

Provence; statuettes based on two female taborers. These are for sale alonside statuettes of men.

 "I am aware that it is something that had never been done before, but women had never voted before, in the end it was achieved and now we see it as something normal and necessary in today's society like ours" 
(source)

 In Spain Pilar Marcos said in 2018: “Right now there are girls playing, they are still few, but when I started there was no one... Today, there are many women, in different spheres of culture, society and work, who continue to suffer discrimination for the mere fact of being a woman.
'they told me what did I do playing the drum when that had always been for men ... they criticized me and did not throw me out, because I left...they said  it was 'a man's thing'... people were very struck by the fact that I was a woman, always out of respect. I only had to suffer that 'contempt' when I started ... because ... in women it is fatal when the drum is played, that cannot be done!

José Ramón Cid Cebrián was interviewed in Spain in 2015:
Q Now the girls play the drum? Before, women didn't play castanets either, dancers played them.
A Now yes, not before, there is some reference to a female drummer, but it was not traditional. There are things that must be maintained and respected, and others not. Why can't there be a female drummer?

21st century, Basque country
Two women txistularis.

Women now join in with men in parades in the many festivals thoughout the region. One woman, Maitane Aurrekoetxea, took the initiative to bring together lovers of this instrument in1999 and founded a new group.

Margo Fontijne plays the pipe and tabor in the early music group Ensemble Corona, based in Holland.