Different things work for different people. Personally, I loved the room that you linked in your post, but I'd also be really happy to have the room that you do. Others, I know, find having so many things visible distracting. Our younger DD is like that - she has ADHD and OCD, so that much visual stimulation just pushes her right over the edge.
If it concerns you, one quick way to make things look neater might be to cover the fronts of the shelving where your fabrics are. You'd then have focal points for your great ladders and hanging basket collection, as well as my favorite - the green ironing station! Love that!! It looks like it might have been a desk in a former life?
Personally, I'm almost green with envy over your space. Like you, I work in the family room. Well, I now say it's my sewing area with a TV and love seat. Problem is, we have a very open floor plan, so when you walk in the door, you are in the kitchen (large, eat-in) with a full view of the room I am in. There is no wall, only a step up to define the space. And although I try to keep it reasonably tidy, my definition of reasonably tidy is not that of other family members who live here.
Oh well, until the basement is cleaned of some of said person's things, I don't really have a lot of options.
I'm going with the a quote from Dr. Seuss: “Those who mind don’t matter and those who matter don’t mind.” Seriously, if this is what makes or breaks a friendship/relationship - then that friendship wasn't worth it to me.
Long story short - it's your space, they are your things and those things are your tools for making wonderful pieces.