Don't believe everything you read. This website got most of their information from the BabySafe movement, which is run by scientists that have been preaching the dangers of wireless radiation to all people for years - even after numerous studies have proven that the danger is not nearly as bad as they are making it out to be. Their science isn't proven, though. It's junk.
In addition, the study the website points to in Scientific Reports was based on 33 mice pregnancies. They kept cell phones powered up near the mice for their entire gestational period - that's a lot more radiation to a mouse baby than it is to a human, especially considering we hold our phones to our head, not our stomachs.
As a matter of fact, only 1 of the studies BabySafe used actually looked at cell phone/wireless use in humans instead of animals. And in that study there were self-reports, which can always screw up your data. Suddenly the mother of an ADHD child remembers being on her phone more when the suggestion is made. So their "evidence" isn't enough to prove this danger.
That said - some caution is needed. We've known wireless devices give us low doses of certain types of radiation for years. You probably shouldn't be streaming that straight at baby. But using your cell phone has not been proven to harm your baby. And shielding products would be taking it too far - you really don't need them.
As of right now I'm no better than the article, though, spouting information. Here's some articles you can look at for peace of mind. All but one are peer-reviewed, scientific articles/journal articles. These are not from just random websites. Some of these are behind pay walls as they are from journals, but you can at least read the abstracts on those and get what they found - that the risk is minimal.
When does radiation become dangerous?
Goes With Previous - if XRay is one of the worst, this should help calm some of your fears.
More Mice! This one found no adverse effects in what would be considered regular use.