Hi Steve,
It sounds like your competitors feel threatened. I did some research and you’re in a fairly competitive area (Deep Ellum) in a competitive city (Dallas), right across the street from what I can assume is the market leader (Common Desk).
It also looks like there have been a few coworking spaces that have come and gone in that neighborhood (Garage, CoHabitat), which only makes local competition that much more aware of the potential for their own demise.
Personally, I would continue being friendly and seek to build your relationships over time. It is reminiscent of being the new kid in school, you’ll get bullied, ganged up on, maybe even threatened. It’s fear on their part, and it’s a normal process.
One way you can appear non-threatening is to pick a tiny section of the market—which you’ve done—and firmly stand by that on your website (which is great, by the way). From reading your website, it looks like you’re competing directly with CommonDesk for the startup market segment, even though when I read an article in which you were featured, you said you were focused mainly on the second-phase companies who are starting to grow their teams and hiring employees. People who value distraction-free work environments, not a high school/college-like cafeteria/workspace.
I would change up your core positioning statement on your website to focus on who you are made for, with something along the lines of, “Coworking for small teams requiring a distraction-free workspace.”
Immediately it will make you stand apart from your competitors, which may put their minds at east a little bit. You’re not going after their coveted start-ups and freelancers. It will also make your marketing that little bit stronger.
I know this doesn’t solve all your problems, but I hope it helps a little. 
I wrote about creating a coworking niche and positioning a coworking space if that helps any.
Good luck!
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On Monday, April 24, 2017 at 2:47:41 PM UTC-4, Steve Floyd wrote:
After slimming down my web design & digital marketing agency, I recently turned my 4500 sq ft office into a coworking space to share resources w/ other people I often work with. I just had my son and wanted to lean down and take the stress levels down a notch from the weekly (sometimes daily) Chinese fire drill of running an agency.
In starting to reach out and network, I received a good deal of hyper competitive behavior from many of the leading community figures in the local startup and coworking communities here in Dallas. I get it, I am the new guy - but I’ve been running businesses in the area (Deep Ellum) longer than all of these people. I get the feeling that there is a tight inner circle in those communities and they push people out they don’t like or approve of. I’ve done nothing to any of them - I haven’t even had a conversation with most of them.
Does anyone here have any advice of how I might overcome this competitive atmosphere?