Your body tends to go into a catabolic state when your blood sugars get low. But they have to get pretty darn low for that to happen. Especially if your body is going to consume muscle mass for energy. To make that happen, you would have to be basically devoid of any other more efficient fuels, like glycogen and fats. Odds of you training yourself to this point? Not very good. If you actually got to that point from cardio, you almost certainly would't want to go and lift weights afterwards, if you were even able to lift at all. Only time your body will consume muscle for food is if you're in a fairly advanced state of starvation. Don't worry too much about losing muscle mass from exercising. It just ain't gonna happen unless you've got a serious eating or compulsive exercise problem.

However, catabolic state also refers to breaking down fats for energy. You can (relatively) easily make that happen, and you'll know it when it happens. You'll bonk out because fat metabolism produces energy at a much slower rate than that of sugar. Probably won't want to lift weights after that either. But it won't break down muscle. (Human physiology major in college, so I mostly know what i'm talking about)

Now, moderate intensity cardio won't make your body go catabolic but it will fatigue you (naturally) and simple fatigue will hamper your lifting performance. But you can certainly make strength gains after a run or a ride. Just not hardcore bodybuilder type gains. Its a trade-off. Is it worth it for you? Thats yours to decide.