Mustachianism actually increased my anxiety initially. Like someone else said, I was constantly comparing myself to others and freaking out that we weren't yet saving 50% yet (almost there; 49% at the moment!), that we were using the car too much, etc. I had to step back for a few months until I got my anxiety under control (it wasn't MMM that was causing it; I'm prone to anxiety and will sometimes just hone in on one thing to be anxious about). Some people are just more prone to anxiety.
Love that your wife can talk to you about things. Using my husband as a sounding board also helped. He would gently remind me that we were still doing really well, that we could always make adjustments to account for the one time we went over our eating out budget, etc.
I saw a therapist as part of my EAP at my last job when I started to feel my anxiety ramping up. We talked out a few things, I guess, but the way she was most helpful was in the physical sense. I know not everyone is the same, but I manifest both mental AND physical symptoms: I tense up, I feel it in my stomach, etc. She taught me to be more mindful of the symptoms coming on, and take a moment to take deep breaths (it's very difficult to remain tense after say, 5 to 7 breaths). I've since taken up Pilates, and even though it's only once a week, it's really helped to put my deep breathing on autopilot for tense situations.
(If it helps, she also suggested writing the feelings down, so I could identify the exact issues and sort of put them to bed, as well as verbally reminding myself that everything has always worked out in the past, and will likely continue to do so in the future. Oh, and I started a gratitude journal, which also helped me realize that regardless of what I was worried about, I also had the same number or more things to be grateful/appreciative/happy about.)
Good luck!