Am I saying you are scientifically illiterate?

Based on the previous statements, yes. However, as a matter of fact, not necessarily insult.

The good news is you're following up with questions and want to learn more, instead of doubling down. With curiosity you will become more literate.

Maybe you were born with all the knowledge of the human race, but the rest of us have to learn it.

The education system in the country you are from has failed you. Assuming you are in your mid-late teens, or older, scientific topics should have already been taught in what North America would call "middle school" (11-14 years old). That teaches you things like conservation of momentum.

There is a reason why it's called illiteracy, because there is an expectation that the baseline level of education everyone in developed countries receives teaches them the fundamentals of how the world around them works. Without this fundamental understanding it's not possible to understand more complex topics that build upon it, stunting growth.

You are scientifically illiterate if you are asking questions that have easily discoverable answers (as in this example, centuries of confirmed results)

The burn from the thrusters doesn't push against space, it pushes against the rocket.

For more easily discoverable answers to basic physics questions, perhaps take a physics 101 course. Or just Google your question.

Or do it the way you just did it... Cunningham's law and all that. But be aware that people will consider you scientifically illiterate if you do it the way you just did it.

Idk what you mean thrust against, but there's always equal and opposite forces. Say you were floating in space and were holding a hammer. You throw the hammer away from you. You will also move away from the hammer as it moves away from you (albeit at different speeds relative to each object's mass). The conservation of momentum.

https://youtu.be/Fp7D5D8Bqjc?si=KyIr0doj2Pinf6U5

Here's an Eli5 video on how rockets work.
https://youtu.be/jI-HeXhsUIg?si=UvtAkVdbPDYimitY

Chemical/liquid rockets and compressed gas thrusters are two different things with different functions. You’re right that lighting a fire in space won’t do much but make a cool firework. A thruster doesn’t so much push against space as it does nudge the ship in the other direction. Newton’s 3rd law and all that except the second “body” in this case isn’t something physical outside the ship but rather the force of the the gas leaving the thruster nozzle causing a recoil.

https://youtu.be/O2QqOvFMG_A