Andrew Linzey's opinion piece sidesteps the context in which both the Old and New Testaments were produced. The founders of Judaism and Christianity were concerned with reforming the behaviour of congregations in their day, not with present day ones. Neither were they going to anticipate the relativistic muddle of late Western civilisation. Had any sort of gay scene existed in 1st millennium BC Palestine, it would have attracted comment.
The paucity of references to homosexuality in the other texts Linzey mentions is because they are concerned with church organisation and the status of the divinity.
Where the Old Testament does deal with homosexuality, it is quite clear:
"Thou shalt not lie with mankind as with womankind; it is abomination".
Leviticus 18.22. A couple of pages later, the death penalty is demanded. As for the New Testament, Jesus gathers people who are aware of the tenets of their Jewish faith and seeks to redirect them to moral rather than ritual behaviours. He thus only attacks hypocrisy. He does not attack aspects of the Jewish faith not requiring reform, and if there is no direct condemnation of gays, neither is there any support.