It don't think it's unfair to point out what "reconciliation" means in the name. We will be reconciled when the days comes that all agree fully with the platform of ReconcilingWorks. Their vision of reconciliation is one of "full inclusion" and "respect for diversity". That requires the recognition of the equal legitimacy of Gay, Lesbian, Transgender and Bi-sexual relationships, etc... For this to happen, the compromise put forward by HSGT would need to be overcome. Whether the goal is to do this voluntarily, by changing opinions, or by adoption of a new policy is unclear.
This is not to accuse ReconcilingWorks of dishonesty or bad faith. On the contrary, they are making their principles and goals clear and are planning to act on them.