His support for heterosexual liberty would be endearing if it wasn't for his past acceptance of the separate but equal civil partnerships:
I do not want same-sex relationships to ape marriage in any sense—several people have used the offensive phrase—because they are different. Although the two share similar elements, they do not have to be identical, so the legal provisions should be distinct. Source
He seems to be offering conflicting messages, on the one part pointing out civil partnerships are not the same as marriage (and also now belatedly, and once he was out of a position to be influential in the matter, calling for marriage equality) but on the other suggesting civil partnerships give additional rights to LGBT folk which is unfair on heterosexuals and this needs to be changed. Indeed, I agree. It's just sad Chris Bryant has taken this long to realise.
Perhaps he doesn't know, it's always possible, but the Government is about to begin a consultation on opening up civil partnerships to heterosexual couples and marriage to same sex couples. Perhaps he might add his suggestions to this consultation. Perhaps he might fight for some legislation to amend the pertinent marriage acts to allow same sex couples to marry at which point he would have a perfect opportunity to also amend marriage law to allow religious texts and readings.
Two birds. One stone. Sadly I think Bryant, as I said in this post, isn't really interested in marriage equality and just gives lip service to it. His obsession with, again, creating a "separate peace" on this issue (i.e. solving just a small facet of the problems of our currently discriminatory partnership rights system, which he helped create and as quoted above approved of), rather than a complete overhaul to create equality for heterosexuals and LGBT people, is indicative of his lack of vision or leadership.
If you feel benevolent and particularly generous, this writer always appreciates things bought for him from his wishlist