In my experience as an up and coming DP equipment absolutely mattered until it didn't. The reality is most clients and would be dp's mistake videographer or camera op for being a dp. I did it starting out as well.
Being a DP is not the same as a camera operator as others have mentioned. It's not the same as being a filmmaker. Technically one can be a cinematographer and not be a DP even. As the defining difference is cinematography is a vocation and DP is a management position within that vocation according to Jim Denault ASC.
When I was starting out equipment was the sole reason I got hired. I knew this and I bought G&E equipment over expensive cameras. I learned the technical side of things and thought I was a DP. It wasn't until I truly understood visual story telling and also learned how to lead a crew that I realized what being a DP really meant. Not coincidentally around that time I started getting hired for my reel and not my equipment. I upgraded to a Red Scarlet and got no more work. Once I learned how to utilize the camera to it's full potential I got more work from my reel. Now I am getting interviews because of my reel and getting jobs because of my knowledge of how visual story works. Nobody cares what camera I have and really they don't care about my reel beyond getting the interview. They care about my art and even more important my personality.
So the short answer is yes equipment matters until you have the experience, knowledge, and network to work on a level where it doesn't matter.
I have asked many ASC dp's and successful movie directors for advice. The same advice is always dispensed. Keep shooting, never give up, and find your unique style. That is something nobody else can reproduce.
You must be able to compare your work to the work of the people getting the jobs you want. You must be able to identify why theirs is better. Having a critical eye and good taste is the real mark of a good cinematographer. You must be an artist if you want to sell yourself and not your equipment. That doesn't just happen because you decide it. It happens by experience. Some people are born with talent. Others must learn it. Everyone must earn their experience and skills to be an artist in demand. That's been my experience and your results may vary.