I can easily link the first and the second third issues. Being anti-capital punishment and pro universal health care are completely consistent views of the expected relationship between individuals and the state.
But on the issue of secular education, I would suggest is only a liberal issue because conservatives have made it so by opposing it. There is nothing particularly liberal or conservative following the provisions in the constitution.
In short maybe the only politics involved with separation of church and state is that politics introduced by the right. One might equally well ask why opposing AGW is a conservative concern.
Under a government which imprisons any unjustly, the true place for a just man is also in prison. Thoreau: Civil Disobedience (1846)
History will have to record that the greatest tragedy of this period of social transition was not the strident clamor of the bad people, but the appalling silence of the good people. Martin Luther King
If there are no stupid questions, then what kind of questions do stupid people ask? Do they get smart just in time to ask questions? Scott Adams