Somebody does not think that something is breaking Shabbos but suspects it may be an issue, yet they don't want to delve into the law because they don't want to stop doing what they are doing and they rely on their logical assumption that it is okay (e.g. melachot not mentioned in the Torah or Talmud; not realizing the science behind the action).
Is this person fully liable under Biblical law (to bring a korban as shogeg, meizid liability, etc.) when they logically believe that it is allowed (even though they are not 100% sure that is the proper law)? If yes, then does it make a difference if a minority (halachikly valid) opinion supports them?
(I would think that there is liability and it is a shogeg because it is not a deliberate violation. However, if they know the science behind it, then they are consciously doing the melacha action; therefore, if they suspect that it is a problem, they may be considered a meizid. On the other hand, the suspicion may need to be an obvious one--like where everyone knows it is a halachik prohibition--to even consider this person a meizid.
The other factor is when a minority opinion supports this person's incorrect view. One can argue that even though the view is not normative halacha, because there is no Sanhedrin there is no liability all together, even if the person is a meizid (there may be other issues in heaven for such an individual, but not connected to chillul Shabbat liabilities). However, one can argue that the future Sanhedrin can retroactively cause liability when they vote on what the law follows. This aspect of the question is a whole other lengthy topic.).