No. It doesn’t. If they were required to avail themselves of those services when abortion or contraception defies their religious beliefs, then yes. That would be impinging on their religious rights. But there is no requirement that anyone have an abortion or use contraception.
In a civilized society, we inevitably pay for some things we don’t believe in.
I believe, for instance, that war is not only futile, but immoral; that belief is grounded in religious tenets that there is that of the divine in each of us. I would prefer not to pay the portion of my taxes that goes into building and sustaining our immense war machine. On a religious level, I don’t believe in it. However, in a civilized society, and one that exists in a complex and often hostile world, I accept that we all have a responsibility to protect our loved ones, ourselves, and our way of life. Just don’t tell me to go out and kill someone. That would violate my religious beliefs. Paying for weaponry and the forces who use them is the repugnant price I pay for the many privileges I enjoy.
And yes, I do recognize some inconsistency here in my stance on abortion and my attitude towards deliberate killing of sentient human beings; but I also believe in the validity of what my mother once said. As a young social worker in Chicago at the height of the Great Depression, she tried to help unwanted children who suffered from neglect and hunger and illness. Years later, she told me, "There are worse things than never being born." Something to think about.