How are these false claims? The executive order directly mentions religious grounds and allows "minority religions" in the 7 listed majority Muslim countries to be allowed in while prohibiting the rest.
It DOES NOT allow minority religions in while excluding the rest.
It does instructs the applicable departments to simply prioritize people facing religious persecution. Prioritizing people through the safety checks and paperwork who are at the most risk should be the EXACT purpose of a refugee program with a humanitarian basis to it.
It's good to go about helping the most vulnerable people. Unfortunately, the proposed methodology in the EO was ham-handed at best, and unconstitutional at worst.
If more than a small number of protesters brought up these kinds of rational arguments, I think many on the right would be far more receptive to seriously listening.
Instead, you hear about a "Muslim ban" and people calling Trump literally Hitler and most people on the right are sick and tired of these kinds of arguments and aren't going to be receptive.