Still I think you are misinterpreting (not strawmanning) Kaj when you assume that he was trying to assert, defend or justify his (liberal) ideological position. I read the post as doing something very different: pointing out reasons why many political arguments naturally fail when both parties have insufficiently compatible base values.

I believe Kaj does not think that there is no difference between the statements "killing people without a very good reason should be illegal" and "homosexual partnerships should be illegal". But he probably thinks that the important difference is a matter of value judgement. Even if I justify the distinct moral status of murder and homosexuality by a more general principle, e.g. that an act is immoral if and only if it causes harm, the justification relies on my fundamental values and is no good in a debate where my interlocutor doesn't share these values.

(I think this should be pretty uncontroversial and politically neutral. Kaj has perhaps made a mistake using the labels "conservative" and "liberal" and expressing where his own sympathies are, which may have created an impression that the article was defending liberal ideas.)