Unfortunately, that survey doesn't seem like something that can be heavily relied on. For one, they only surveyed women. It's unclear if the men in the same household would give similar or different estimates. They also don't define what is meant by "influencing" a decision. When you try to go to the link to learn more about the survey methodology, the link redirects to https://breastfeeding-mom.com/ instead.

I think the BLS is probably better data.