I'm stuck behind red tape.
This would refer to your being stymied by bureaucracy. Without the article, "red tape" refers to the concept--excessive bureaucratic requirements.
I'm stuck behind the red tape.
With the article, "the red tape" refers to specific red tape. In your sentence, someone who didn't know the context might think you were referring to physical red tape, such as might be used as a cordon.
But it could also refer to a specific bureaucratic nightmare: "The red tape at the license office is brutal." In that context, the identification of the specific bureaucracy would typically be in the same sentence or a preceding one if you use the article.
But you can talk about the concept in a specific case even without the article: "Red tape at the license office is brutal".
In your example, the article wouldn't normally be necessary because the meaning is clear without it (perhaps clearer, because it would be obvious that you were referring to the concept). If you were calling someone who had no idea where you were and you wanted to let them know you were delayed, you could say, "I'm stuck behind red tape at the license office." The article wouldn't typically be used in this context.