Make sure your stylus is clean.
The chances are that the cartridge is not properly aligned in the headshell. I realize that the MMF turntables come with them already installed, but nothing is foolproof. The cartridge alignment should be checked with a tool.
The anti-skating could cause some problems, but it sounds like mis-alignment to me. Just to be sure, you could set the anti-skate to the same amount as the cartridge tracking force. This may or may not be perfectly optimal, but it is a good starting point, and should not be causing distortion at that setting, to the amount you are describing.
If you don't have a cartridge alignment tool, this is something that every analog user must have. There is a good one for only $20 at www.turntablebasics.com and it is the same one I use.
This will set cartridge alignment and overhang, and either one of these settings being out, could cause the problems you are hearing.
What is happening to you is not terribly unusual, and I have seen some other threads about it on these pages. The vast majority of times, it is solved by checking and re-setting the alignment and overhang with the proper tool.