I've been spending a ton of time on "Photography Youtube," that weird section of the site that is devoted to photography as art and business. There's a lot of good information: product reviews, techniques, lightroom tutorials, etc.
Then there are the opinion posts where some guy (it's 90% guys) is arguing about how something "in photography" is dumb or whatever. I've seen videos bashing other photographers, bashing cameras, bashing trends, etc. Which is also fine, though it's pretty tiring to watch more than two of them.
One thing I noticed, ironically, in all of this complaining and arguing was that "no one cares how you get the shot" which has to be patently untrue. Or maybe it is true, but it's true in a way that the producers of those videos aren't anticipating.
In this example, since it's kind of dear to my heart, we'll talk about shooting on film. Do most people care that you shot on film? No. And I think it will actually be a hindrance to certain forms of photography. It's very difficult to shoot analog and cover newsworthy things, the turnaround time is abysmal. I'm sure you're getting really good shots, but news is digital and immediate. I know that when it comes down to it, I better pack my DSLR for things that are "live."
By "live" I mean things that have a known (and time sensitive) interest level. When I go to shoot protests, I'll bring my DSLR. When I go to comic conventions, as much as I hate being a part of that herd of shooters, I bring my DSLR. I still bring the film cameras too, but I know I will need the flexibility and immediacy. That's just how it is, and I want to be a part of that stream.
Now, that also gives you a lot of leeway for times when analog photography is perfectly adequate. When you're shooting portraits and you're working on a looser time table you can get the shots one day, develop them that night, scan them the next morning. It's nice. It's a longer flow of production with some natural breaks thrown in. By the time you're sitting down to edit, you've removed yourself from the photo session itself and you can be a better judge of the images as they stand. As an added benefit, you don't have someone potentially pixel peeping over your shoulder.
Quick aside: One of the things that I believe will make you a better photographer is to turn off instant review on your DSLR. When that LCD screen lights up after the shot, I'm far more tempted to look at it. Know your settings before you shoot and you're 50% there.
So, to the degree that your workflow dictates your turnaround time, people DO care about how you produce images.
I also think that there is a level of care in that people value the creative process more than they often let on. It doesn't "matter" whether an artist works in one medium or another, but that choice in itself informs the work. So yes, when you choose to shoot on film or digital it does matter. In as much as it matters whether you travel by train or by plane. The experiences are totally different and important.