The Lib Dem document on transphobia is an oddly framed thing (influenced, it says, by stonewall).
First, it appears to mean that acknowledging the law found in the gender recognition act 2004 is transphobic.

Section 9 of the 2004 Act which provides for the effect of a gender recognition certificate is that a person's gender becomes the gender acquired by the GRC subject to the terms of the 2004 Act or any other legislation.
https://www.legislation.gov.uk/ukpga/2004/7/section/9

This includes sport
https://www.legislation.gov.uk/ukpga/2004/7/section/19
This means that someone with a GRC (never mind someone who self identifies) is not treated as the acquired gender for sport.
Under the lib dem document agreeing with the law, and sporting bodies who support this is transphobic.

The equality act 2010, sch 3 para 28 provides that single sex spaces and services can be provided, and can lawfully exclude those with the protected characteristic of gender reassignment (which includes those who self identify and those with a GRC). https://www.legislation.gov.uk/ukpga/2010/15/schedule/3/part/7

This allows a counselling service for women survivors of domestic or sexual violence to take a trauma informed view and exclude male to female transsexual people https://www.legislation.gov.uk/ukpga/2010/15/notes/division/3/16/20/7/5
Under the lib dem document agreeing with this law and supporting this approach is transphobic

The lib dem document comes from their disciplinary subgroup and will be key to the party disciplinary procedures. https://www.libdemvoice.org/liberal-democrats-adopt-definition-of-transphobia-65868.html

To support the existing law would then, under this document, be transphobic. Supporting the existing law could be a disciplinary matter under the Lib dem disciplinary processes.
This is ridiculous.

The equality act 2010 is framed in such a way that in various places interests of those with different protected characteristics clash. The Lib dem document in effect prioritises the gender reassignment characteristic in all circumstances where interests conflict.

I am not clear how a Lib Dem controlled local authority can effectively exercise its discretion under law when providing various services which might see rights conflict when a party document requires them to prioritise trans rights.

Having used trauma services I am deeply uncomfortable with anyone effectively stating that a trauma informed approach for the service users at their most vulnerable should be condemned as hateful and based on fear and dislike.