This is untrue. What makes it seem true is that there are extremely bad or nonsensical arguments that some people will accept (often without examination) when they support their own predetermined (often by lifestyle) side, but they will be far more critical of
any argument that supports the other side. They spot the bad arguments on the other side and call them out, but
ignore the good ones because they cause stress.
The best way to notice this in yourself (I think) is if there are arguments for the other side of an issue that you simply avoid discussion of altogether. When they are brought up, you attack the source, personally attack the person repeating them, or refuse the discussion on some other terms. This is reflexively doing propaganda, on a small scale, but as a reaction to being cornered.
If you find yourself in this situation, resorting to repeating slogans you've heard rather than treating the argument exactly as you would treat an argument in an uncontroversial context, it's better to shut up, listen, and reflect.
The only moral position is to be a collection of any valid argument you can find, always trying to clarify their degree of soundness. Whenever you deviate from that, you're defying reason, and weakening civil society (which relies on secular protocols.)
If you consume propaganda with that mindset, you notice because it has very little useful content at all. It's astounding how long media can go on about a subject without saying anything, or making any coherent claim, and scary when you see people who seem to get something out of that avalanche and they can't quite explain how they got there. It's how Saddam did 9/11.