How do her actions affect the rights of someone else? Giving a child up for adoption is legal. It's legal for an agency to advertise that they have a child available. So the only illegal thing that the woman did is to use Craigslist to offer the child for adoption. That's a restriction on speech that isn't content neutral (the content of the speech is what is regulated), that doesn't serve a important government interest (because there is no law against person to person adoptions in Texas, and the woman wasn't offering to trade anything for the child), and the restriction doesn't leave many other channels open (it's fairly difficult to get a message to a large number of people without using any "public media"). The law fails 3 out of the 5 tests that make up intermediate scrutiny, which is the standard that courts use to determine whether or not a law in constitutional.

I'm not saying the law isn't ridiculous, but it makes it impossible for there to be competition between adopting parties. While I'm not familiar with Craigslist, it seems to me that she put the child up for adoption there in the hopes (misguided or not) that she would find the "best" adoptive family. The law that you linked says she cannot do that (at least under private adoption). You may have evidence that the law is wrong, but neither of us are judges (at least I'm not) so I don't think we can exactly say that the law should be abolished. The problem stems from the fact that there does not appear to be active interest in placing a new law for the adoption process. The linked PDF even says that private adoption is an option only because the state felt that individuals should retain some rights in deciding the fate of their children.