No, we don't hate the free press. However, we condemn propaganda outlets with a clear bias against certain demographics. Being supportive of the free press doesn't mean that you have to agree with everything and anything that's being produced within the framework of what constitutes the free press.
And, yes, there are all the reasons NOT to be immigrant bashing: They are a very vulnerable demographic, of which many have either little or nothing materially speaking, and are disadvantaged as far as rights are concerned as well. These are people like you and me, just in a precarious situation, a large demographic of people whose sole common trait is that they're migrating from one country to another. Apart from that, they're individuals with all sorts of backgrounds, values and personalities.
The only reason to be bashing immigrants in their capacity as such is bigotry, as there's nothing that connects these people except their situation. Unless, of course, your reasons have something to do with the distribution of points of origin of the immigrant demographic you're considering, in which case the same logic applies: Vastly different people, only connected by point of origin, which means, again, there's only one possible reason for bashing them: Bigotry.
RE: Fox Interrupts Immigrant Bashing to Report Anti-Immigrant Shooting