It's a challenge not to be super annoying about it at times, and I'm always a bit self conscious about it when posting.
My thoughts are the best way to promote a thing is to be indirect about it. Getting excited about the plans you have for it and letting people know, "Big plans in the works, guys! We're revamping our Patreon and will be offering even more cool stuff that I can't wait to show you!" Or getting excited about things being offer, "Holy cow! We just received our shipment of buttons for the $1 and up Patreons and they look so good! [insert picture of said buttons]" or "Just finished a bunch of sketches for you lovely Patreons out there. Thank you so much for the support! [insert picture of sketches on a drawing table]" so on like that, maybe.
Make it more of like a status update than a self promotion thing. Those are more enjoyable to read and fun to see the lovely the cool stuff people are receiving through supporting you.
So many non-artist normal civilian people have the idea that art is/should be free and it's a hobby, not a career. However, all of us that are seeking to make it a career are actually, and should be considered as, entrepreneur launching our small businesses. We do all the same things as other entrepreneurs in other fields do; worry about getting our names out there, copyright, promoting, making a sustaining living off of what we love, quality control, time, taxes, hiring help, thinking of new ideas to make it happen, niche marketing, overhead, print cost, on and on we're the same. We are creating our own job, and the day job is just there until the job we're creating takes over. Which just takes time to grow.
I don't get too concerned over trying to convince these people that art is more than a hobby. I have too many other thoughts and ideas brewing on how to launch my career to let them distract me. 
Either they'll want to support me and join my wacky fun journey or they won't and will just want to keep reading for free (which actually they'll still support me indirectly through ad revenue $$$), either way it's all good, and I'm still making art.