Should I still submit a manuscript to a journal if a member of the editorial board is advancing a competing theory that is incompatible with my work?
Many journals will allow you to suggest a handling editor, and pretty much every journal will allow you to specify reviewers that you believe should not review your paper due to conflict of interest.  This is an appropriate situation to invoke these options.

Depending on the particular forms the journal uses for submission, the right place to put an explanation of your concern may be either the submission forms or the cover letter.  You do not need to go into much detail, simply saying:


  "Editor X's student is working on a competing model, so I am concerned about bias."


If you are dealing with an honorable journal, that should be enough: this is an entirely normal and reasonable concern you should not have to back this up with published evidence (people understand that scientists talk, pre-publication), nor do you need to denigrate the character of Editor X in any way.  They have many editors for a reason, and many possible reviewers they can draw from as well, and every good scientist understands that it's usually better to be safe than sorry when it comes to dealing with conflict of interest concerns.