Can a roundtable chair not liking my research influence my chances of having a submission accepted? I believe that a roundtable chair at an upcoming conference does not like my research. I would like to submit an abstract in response to the call for papers. 

Does the roundtable chair play a part in the selection process, or is it solely the task of the conference committee?
There is no way to anticipate if a roundtable chair will be on the conference's program committee without more information.  Most conferences list their program committee on the conference website.