Adam Thomas, 22, and Claudia Patatas, 38, were found guilty after a trial of being members of the extreme right-wing organisation National Action, which was banned in 2016.
A jury at Birmingham Crown Court heard the couple gave their child the middle name "Adolf", which Thomas said was in "admiration" of Hitler, and had Swastika scatter cushions in their home.
Photographs recovered from their address also showed Thomas cradling his new-born son while wearing the hooded white robes of a Ku Klux Klansman.
In conversation with another National Action member, Patatas said "all Jews must be put to death", while Thomas had once told his partner he found "all non-whites intolerable".
Former Amazon security guard Thomas and Patatas, a wedding photographer originally from Portugal who also wanted to "bring back concentration camps", were found guilty after a seven-week trial.
Thomas, a twice-failed Army applicant, was also convicted on a majority verdict of having a terrorist manual, namely the Anarchist's Cookbook, which jurors heard contained instructions on making "viable" bombs.
The couple, of Waltham Gardens, Banbury, Oxfordshire, are set to be sentenced in a two-day hearing starting on Friday, alongside four other men.
Daniel Bogunovic, 27, of Crown Hills Rise, Leicester, a leading member in National Action's Midlands chapter, was also convicted of membership after standing trial with Patatas and Thomas.
Three others; goods vehicle driver Darren Fletcher, 28, of Kitchen Lane, Wednesfield, Wolverhampton, IT worker Joel Wilmore, 24, of Bramhall Road, Stockport, Greater Manchester, and van driver Nathan Pryke, 26, of Dartford Road, March, Cambridge, all admitted being National Action members before proceedings began.
The sentencing hearing, presided over by Recorder of Birmingham Judge Melbourne Inman QC, is scheduled to last two days and will conclude on Monday.