The acceptance into Christian groups of abortion and other sins is one effect of the relativistic and hedonistic world views which are promoted by the secular governments of today.
Plus, when a government treats all religions in the same way, it is indeed a relativism of truth, because religions make exclusive truth claims. If one religion is right in one matter, the others are wrong.
Fueled by the false notion that the truth is subject to democratic vote, the modern government will adapt its laws to whatever the majority wants (ideally, at least). Thus we have complete relativism: in treatment, in truth and in morality.
You are right that the dream of many atheists is to have a government which actively persecutes religion. And history makes that evident:
First, the French revolution slaughtered thousands of religious people, curbed the rights of the Church and instituted their own civil mock-religion.
But of course, the people of Europe, at that time, still did not accept such a radical posture. Therefore, the newly founded French government adopted the relativistic stance (and so the rest of Europe followed), instead of actively denying religion.
The next step was the socialist revolution. What the bloody revolutions of the previous age had not the power to do, these even bloodier revolutions did: prohibited religion.
Thankfully, the horrors of socialism could only be endured for so long; and nowadays it is but a sad memory on the minds of those who lived under it.
But he is very naive who thinks those who conspire against Christianity (even if unconsciously) were satisfied with relativism. Even though atheistic revolutions now seem a lot less likely (though guerrillas are being fought as we speak in continents such as mine), the mentality which inspired them is being spread.
And here is the point in which we realize that under the guise of indifferent relativism, the modern State and the modern mindset deny traditional Christianity and do not tolerate Christian values.
The extremely secular mentality of the French revolution is still alive, only now it is a lot more popular. And the modern State reflects that, by passing ever more anti-Christian laws. And many Christian groups give in to it, and with it reject everything that Christianity was traditionally connected to, hence your association with abortion and Christianity.
There's probably not one vice which some Christian denomination today does not condone. But that doesn't mean they are Christian at all.
This illusion that Christianity has become more bland and tamed is an effect of the growth of atheistic secularism, which now has gone from torture and murder of Christians to the unconscious conversion of them to the relativistic values of total equality and liberty.
The government gives people the freedom to be religious and not be persecuted (I am here typing all this and attending my church with no fear of being shot for my beliefs), but through its laws denies Christianity. It is impossible for me, as a Christian, to be in favour of my completely secular, relativistic, demagogue and quasi-socialist government.
Governments such as ours which take no religious stance have already taken the stance against religion.