The Church is you and me, but there is also the institutional structures of the Church. If you as a private citizen want to pay for someone else's contraception, by all means do so.  The institutional structures of the Church cannot do so.  We believe that contraception is sinful.  To that end we cannot do anything to enable sin.

Whether you like it or not, the US Constitution protects religious freedom.  Religious freedom is going to affect people.

I certainly care for the rights of women.  When a women wants a medical procedure done on her that does not affect someone else's life, I don't care what she wants to do.  If a women wants to have her Thorax taken out, by all means let her do it.  If a women wants her gall bladder taken out, let her do it.  If a women wants to cut off her leg for whatever reason, by all means, let her do it.    

Abortion does not just affect the woman.