'change who can access changing rooms, toilets, shelters' - theoretically orgs can invoke a single sex exemption according to the EA. And a GRC has no impact on that. In practise, nobody seems to invoke the exception and we have de facto self ID - see the CEO of a rape crisis centre who is a male without a GRC, etc.
'impact on who can compete in sports teams' - probably true, this is all down to individual sporting bodies, and varies but is based either on biological sex, or on testosterone levels.
'change people's ability to alter name and gender on passports' - I'd imagine making it easier to obtain a GRC would make it easier to change other documents, but then it seems people often work in the opposite direction, changing documents in order to obtain a GRC.
Some of the issues with the Scottish proposals are:
If a male has a GRC they go to a female prison, without risk assessment or any other checks. They are treated EXACTLY as a female.
Lowering the age to 16. For obvious reasons.
Removing the requirement for a medical diagnosis fundamentally changes our understanding of what 'changing sex' is. It presents sex as something we choose according to an indefinable inner feeling. Yes, we already have de facto 'self ID' operating in many situations, this is what has led to males being housed in female wards in hospitals, mixed sex changing rooms, etc. This is has led to sexual assaults, voyeurism, and women self excluding from various services and groups.
The reforms have taken no account of the many people who raised issues - for example women of various faiths who are forbidden from sharing spaces etc with males, disabled women who require female only care, women with PTSD who are triggered by males, etc. All of these issues were raised, but all seem to have been so far dismissed.