My work mobile is on the EE network and doesn't appear to have any issue with adult content. The industry I work in requires me to access explicit content occasionally and I've yet to come up against any roadblocks with EE.
EE is branding confusion hell. They're a result of the merger between Orange and T-Mobile, but depending on situation you'll either have them treat you as an "EE customer" or as a T-Mobile/Orange customer. The only ones who are "only" EE customers in their eyes appear to be 4G users.
My contract was entered into with T-Mobile, and is a personal account, and I have never seen a block, including testing just now with obvious candidates.
I'm on T-mobile (though my phone shows EE as the network) with a 3G monthly contract and I've seen the block message. I can't remember what it was, but it wasn't porn, just some random link I followed that I didn't care enough to work around the block to see.