Contraception is a public issue, and therefore I support public funding for this. It is a lot less expensive to pay for preventative measures of population control than to pay welfare costs. It costs the public money to support those born in poverty more than it does to prevent people being born into poverty.
So you might as well provide a means of preventing pregnancy if the people having it aren't trying to get pregnant, which in most cases they aren't. Making something that's going to happen anyway safer isn't a question of morality, it's giving people the option to be responsible should they choose to be.
Contraception is not only a measure of public health and population control, it's also a very basic health need. If we can provide public funding for medicines like Viagra to improve sexual performance, then it is only logical that we provide public financing for different forms of contraception as well.
Contraception should be funded for those who cannot afford it. The alternative is that the poor and uneducated have children they cannot support and as a result must depend heavily on public assistance. This in the long term is much more expensive than any funding for contraception. Furthermore, children born in poverty are much more likely to become involved with crime and other social ills.