"I'm not going to intrude on your marriage" or "I'm not going to eavesdrop..." might be a better way to re-phrase the meaning of this one.
The spirit of the phrase is that the other people's marriage isn't the business of the one speaking, and so they are going to stay out of it.
Remember that tip-toe means to walk on the tips of your toes, which you do in order to walk very quietly. Thus, you're trying to either spy on someone, sneak up on them, or not disturb them.
A more common use is "I'm not going to tip-toe around it, so let me just say it." This means that you're not going to try to be diplomatic, but rather very direct and blunt.