With First Minister Peter Robinson having claimed republicans are perceived to receive better treatment than loyalists, Mr Justice McCloskey stressed the separation in judicial and government powers.
His caution came as it emerged that Bryson was arrested in a converted attic of an associate pastor's home.
Bryson, 23 and of Rosepark, Donaghadee, Co Down, is the reported chairman of the Ulster People's Forum, which was set up in the wake of protests over the decision to limit flying of the union flag at Belfast City Hall.
He is charged with six offences involving encouraging or assisting offences, and taking part in an unnotified public procession.
As he appeared by video-link from Maghaberry Prison, a prosecution lawyer told the High Court that a decision was taken to detain him after police studied video footage of him addressing crowds of demonstrators and allegedly encouraging them to offend.
A search operation at his home proved unsuccessful, and he also escaped police after being spotted in Kilcooley, Bangor last week, it was claimed.
"When they did attempt to apprehend the applicant at the home of an associate, the associate attempted to prevent police from gaining entry into the house where they found Mr Bryson in the converted roof-space bedroom," the lawyer said.
The judge was told how the accused posted comments on social media sites as the PSNI hunted for him.
"He said the police weren't very good at their job because they haven't arrested him," the barrister said.
At one stage in his posting Bryson claimed Chief Constable Matt Baggott needed to use better tracking devices in a bid to locate him.
The barrister added: "He indicated he might hand himself in if he could walk. He said his legs are sore."
She claimed if released Bryson would re-offend and encourage others to do so through his speeches.
Setting out the estimated £20m cost of policing the flag protests over the last three months, she added that the demonstrations have resulted in serious public disorder, injuries to police and significant losses suffered by the business community.
Defence counsel Richard McConkey argued that his client can be seen in the footage liaising with police to ensure no trouble breaks out at protests.
"At all times Mr Bryson has been encouraging peaceful protests," he said. "There is absolutely no suggestion at all that this man has been asking people to behave in an unlawful manner."
Mr McConkey contended there was confusion over police now declaring that unnotified processions to City Hall were illegal.
However, Mr Justice McCloskey refused bail after backing prosecution submissions that the accused may re-offend or incite others to do so.
"The applicant, who has openly evaded and obstructed the police previously, thereby showing no regard at all for the criminal justice system, may by virtue of that conduct repeat his previous behaviour of this kind," he said.
In his ruling the judge stressed that every bail application was different, adding that anyone attempting to compare cases has a responsibility to ensure they are fully informed of all the facts, circumstances and merits.
A proper comparison can only take place in a courtroom, he pointed out.
Mr Justice McCloskey warned: "Where there is ill-informed debate involving comparisons between individual cases this simply engenders confusion and misunderstanding.
"It can also have very serious consequences, it can serve to jeopardise the delicate balance of the separation of powers between the judiciary and government, and in doing so it can undermine the rule of law itself."