Never a problem. A few months after I got it, about 6 years ago, I made my first, nervous flight to Frankfurt. Leaving Dublin, nobody did anything different - walked straight through the scanner, no pat-down. Coming back, German security was a little more robust, maybe because of the Air Iran plane beside ours! After the walkthrough scanner, I was given a quick pat-down then directed to follow the security guy to a sort of "tent" within the area where nobody could see us. There I had to remove my upper clothing, he took a quick look and said that's OK. Then he apologized very sincerely, poor guy looked quite embarrassed, and offered his hand (it's Germany - they shake hands a lot!) which I was happy to shake. That was it. Oh - the female guard watching us with her hand on her holstered gun then exited stage left!
Since then I've made a few flights to Germany and Estonia and there has been absolutely no hassle or even a question when they do a pat-down. It's like the word has got around and they can detect or identify someone with a stoma, all quite routine and discreet. I've never had to explain, or offer that card that explains in half a dozen languages. Better training, or maybe it's just that there are more of us about than you'd think? Don't worry - you'll be fine.