I think this goes with the belief that when you start talking about something, be it a relationship, a goal, or as you say a plan, there's a good chance that it may be jinxed. However, there is no scientific evidence that being jinxed is real. Rather, it all lies in the inherent uncertainty that a plan will be executed properly. We don't get to see the problems that lie ahead us; hence, we often associate this thought of having to tell it to other people, as the culprit for why our plans fail.
I do believe that having real faith in your plans can counteract this anxiety. Having positive attitude/outlook in life and carefully planning every step of it may actually help in realizing your plans.
When talking to other people, seek advice from those you think have more experience in dealing various consequences. In other words, you also need to choose who you talk to. Do not waste your time arguing with people who always have negative things to say. The last thing you need in your life are people who will tell you, "I told you so." after having to learn your failure. Rather than discouraging you, they should be the ones who encourage you to go ahead with your plans, and be there for you when these plans fail.