It should come as no surprise why the republicans are opposed to the Obama administration's mandate for contraception coverage and it has nothing to do with "moral objections". The issue is about what it's always been about for them: MONEY. I mean seriously, when have the republicans ever really objected to anything on moral grounds unless they stand to gain financially? More below the squiggle.
Portraying President Obama as an overreaching dictator set out to destroy religious freedom is just a bonus for them, but what it really is is a cover. The private health insurance industry (huge republican backers) are the ones really behind the opposition. If an employer or an insurer has the power to deny coverage based on "moral objections", then both stand to gain enormously and the republicans will be there to pick up the crumbs (campaign cash). The language of the legislation proposed allows employers and insurers to deny coverage on a range of "questionable" situations. For example, they could deny coverage to same-sex couples, or deny coverage to children born out of wedlock, interracial couples, people with drug addiction, even people of different religions.
When it comes to the insurance industry, there really is absolutely no level to which they will not sink to when it comes to denying people coverage.