One of the major differences between the right and the left concerns the question of authority: To whom do we owe obedience and who is the ultimate moral authority?
For the right, the primary moral authority is God (or, for secular conservatives, Judeo-Christian values), followed by parents. Of course, government must also play a role, but it is ultimately accountable to God and it should do nothing to undermine parental authority.
For the left, the state and its government are the supreme authorities, while parental and divine authority are seen as impediments to state authority.
Let's begin with God.
From Karl Marx -- "man is God;" "religion is the opiate of the people" -- to today's left in America and elsewhere, God and God-based religion, specifically Judaism and Christianity (Islam, too, but in the West, Islam has played little role) have been the primary obstacles to leftist victory.
That is why the further left a government or an ideology, the more it has opposed religion. The first targets of Lenin and Stalin were churches, synagogues and clergy. At the modern Western university, the epicenter of leftist ideology, the same has held true. A clear, if unstated, goal of modern liberal arts education is that as few college graduates as possible hold values rooted in traditional Judaism or Christianity.
This also explains the left's passion about maintaining and furthering secularism -- under the banner of "separation of church and state." Anything -- any value, any idea, any person -- rooted in Judeo-Christian values must be confined to as narrow a place in society as possible.
That is largely why there is such intense leftist opposition to the pro-life position. Since most opposition to abortion (when the mother's life is not threatened) emanates from religious values, "pro-life" means that transcendent values are authoritative, not a woman's wishes.
It is the major reason for left-wing loathing of those who oppose embryonic stem cell research: That opposition usually emanates from religious sources and therefore places Judeo-Christian values higher than science's capabilities.
It explains leftist opposition to even mentioning God in public schools -- students must graduate as secular as possible.
It is not secularism that animates those positions; it is leftism.
One proof is that there are many secular people who are not on the left. Prominent examples include Wall Street Journal editorial and opinion page writers and the Washington Post's Charles Krauthammer.