Canberra's Hyatt Hotel says it supports gay and lesbian equality, amid growing criticism of a conference organised by controversial anti-gay marriage campaigners the Australian Christian Lobby.

Opposition Leader Bill Shorten has come under pressure to withdraw from his keynote speech to the two-day conference, which will also include speeches by incoming Sydney Catholic Archbishop Anthony Fisher, Assistant Immigration Minister Michaelia Cash and Labor backbencher Shayne Neumann.

Critics of the group, known for its highly organised and well funded political campaign against same-sex marriage in Australia, have targeted the Hyatt Hotel on social media this week.

The criticism comes one year after the ACT Legislative Assembly passed historic same-sex marriage laws.

Wednesday's anniversary of the passage of the laws, overturned by the High Court in December, will be commemorated in a motion before the Assembly chamber.