That would only be true is you believe that the Right has not been doing their job of shining a light on the Left's ugly side. As far as I can tell, the right has done a very good job calling out the left one any and all problems in their party, it is just that the problems the left have, and they do have some, are quite minor in comparison.
Please understand that SPLC labeling them a hate group, or pretty much anyone labeling anyone anything else, does not prevent them from existing in the United States. The Ku Klux Klan still exists and openly holds meetings and marches in the US. The only time it becomes an issue is if they break some pretty specific and very narrowly defined laws, or if the US Government is doing it directly. Neither is the case here, so both sides are welcome to call each other anything they want all day long.
I know, free speech in America is kind of wild. You can say just about anything to, or about, just about anything and it is acceptable and even considered normal. The SPLC calling people terrorists or hate groups is normal and happens all the time, the only time people care is when they have a point. Which in this case many people think they do.