Separation of Church and State, as far as western democracies go, does not mean that religious leaders and organisations cannot hold political views or endorse political candidates. It does not even mean that the Church cannot take part in politics.
Indeed, the Church is a powerful player in politics, eg. US Presidents have mainly been Protestant and not Catholic, and religious leaders, eg Reverend Jesse Jackson, have even been nominated as running mates for US Presidential Elections.
For them, separation of Church and State means that they are a democracy, not theocracy; that there is no one State Religion; that there must be religious freedom; and most importantly, that the Govt cannot interfere in the affairs of religious groups, tell them what to teach, what not to teach, what is deviant teaching, etc.
For Singapore, however, the direction of the PAP is to muzzle all religious groups, to the extent that they can’t make any kind of statements against Govt policy. So even on matters such as abortion and contraception, which the Catholic Church feels strongly about, they could not say anything publicly against the PAP’s Two Is Enough policy.
Hence, the anxiety and fear of the PAP govt when it heard that the Archbishop had written a letter of support to Function 8.
I leave it to readers to consider which model is better for Singapore.