There seems to be a potential clash between the right not to be be discriminated against on grounds of transgender and right not to be discriminated on grounds of sex (and I mean sex as defined by sections 11 and 212 of the Equality Act so biological women and those with GRC, not those just starting or going through transition)
So for example take a scholarship to encourage women onto STEM subjects. A transitioning transgender women, if prevented from entering, may argue that they are a women so if they are excluded it is indirect transgender discrimination.
A biological women, if overlooked in favour of transgender women, may argue that the purpose of the award is to overcome the barriers to STEM brought by years of social conditioning and opportunities denied to girls which they would have (and a transgender women brought up as a boy/man would have not had such barriers).
I suspect the clash will actually come with regard to single sex sports activities or service provision like hospital wards which women campaigned for years to achieve. If, as we see from the actions of the Girl Guides, the British Swim Association, and service providers like Top Shop, transgender women are permitted access to these spaces even if they have not physically transitioned. There are obvious concerns such as the social conventions about public nudity in, for example, sex-segregated swimming pool changing rooms.
Currently the campaigning by transgender activists fail to see that women may themselves have an indirect sex discrimination claim against a service provider who (by allowing in physically intact males into single sex locations) prevent them from using the service, because as biological women they have concerns for their privacy or safety.
There have been other clashes of protected characteristics, such as the Ladele (marriage registrar) case or the "gay cake" case. Ultimately the courts or Parliament will decide who will prevail. I cannot predict how this will play out