Specifically with the contraception issue, the argument most religious groups made was that it was an encroachment on their religious freedoms, forcing them to perform an action which was morally wrong to them (or for some groups, like Jewish ones who have no issue with birth control, simply that it was encroaching on religion in general). In other words, they're implicitly agreeing that government can make certain regulations on behalf of the people as a whole, assuming they are acting in the interests of the people. [And there are other groups who disagree with that basic premise in general.] It just happens to be that in this case that public interest is trumped by the interests of religious freedom - something people on the left disagree with.
Santorum, however, is making a different argument: Whether or not one feels that government interests should trump religious ones, and perhaps even if one would agree to that, in this case the government is actually acting against the interests of the people it is trying to protect and assist. It is his belief that birth control actually harms women (and men and particularly children) because of the consequences of living in a society which has birth control readily available. This is not an argument about government intervention or government interference with religious freedoms in Santorum's eyes; it is an argument specifically as to the merits of the intervention which is being proposed.
[Note: I don't necessarily agree with the various opinions, just find them interesting.]