I think it is worth considering the relationships between power and authority. The authority of the church brings with it a certain amount of power, but some leverage the situation to acquire far more power. The judiciary, for example, has its own authority and related powers, and yet can be cowed by those with greater power. Does the exercise of judicial authority act as a restraint on those with power, or does it become a tool of those with power to protect their actions at the expense of others, those targeted for victimisation?
One example of power and its limits in The Crucible comes in the death of Giles Corey. He is being tortured by pressing and no doubt his suffering is extreme. His death is inevitable, both literally and figuratively under the pressure that those in power can bring to bear, and yet all he says is "more weight." He retains the power to remain true to his convictions, to refuse to step back from defending his wife even under threat of death, and he does. In neither confessing nor denying the charges of witchcraft, he ensures that his sons can inherit. His love for, and loyalty towards, his family give him a strength to resist the pressure, He has the power to choose to do no further harm than he has already (inadvertently) done, and he makes the choice to die in agony and to gift them what little protection that he can. To me, this is example related to the context question: Corey demonstrates that, in a circumstance where he is physically powerless, he retains the power to make choices and to act so that his family gains something from his sacrifice. He is also influencing how he will be remembered, as an exemplar of the power of character even in the face of brutality.
Miller's own experiences before HUAC mirror the experience of Corey. Faced with a demand to name names or be jailed for Contempt of Congress, Miller refused and was fined, blacklisted, jailed, and disallowed a US passport. Miller's words, "I could not use the name of another person and bring trouble on him," echo Corey's circumstance where his actions have likely condemned his wife and he is refusing to add to the harm he has already caused.
The play illustrates the growing excesses that come with authority and the use (and misuse) of power. Rev. Parris, concerned for his own status, takes step after step along this road. Rev. Hale is motivated by his crusade against witchcraft and enjoys the respect and influence he gains, but ultimately his motivation is not personal gain and the abuses of power and the corruption in the trials disillusion him. Danforth is very much the opportunist, using the opportunity to gain in power and influence at any cost. Hale illustrates one approach to seeking justice (at least in some form) even when he lacks (relative) power.
Misuse of power and injustice ultimately lead the majority to be outraged / horrified and to turn away from the proceedings. The trials end and the people are left to recover and rebuild, having learned that the justice of the mob is not justice, that power corrupts, and that failing to recognise and act in the face of wrongs perpetuates them. The consequences of HUAC are clearly paralleled... having gained so much power and wielded it injudiciously, the Committee overstepped to the extent that the corruption in what was happening became clear.
There are parallels in other areas where power has been held so long that the only consideration becomes "can I" rather than "should I"? The current issues with racism at Collingwood is a recent example. Eddie McGuire has been President so long and been able to obfuscate around racial issues that a report demonstrating systemic racism became a PR problem rather than being dealt with as the call for change that it was. Héritier Lumumba, the subject of racism who was disempowered and ostracised for raising his mistreatment, has been vindicated - a step towards regaining power and achieving some measure of justice.
These questions have a great deal of scope to address narrowly (in the context of the play and its allegorical story of McCarthyism) or much more broadly. Power often comes with being part of an "in" group and leads to disrespect towards and mistreatment of "out" groups. Othering is a powerful part of that - when others are not part of us, they are dehumanised to an extent, making the mistreatment allowed (in some sense) or shielding us from empathising with the suffering we inflict onto them. Othering can also be used to oppose steps of reparation and reconciliation, labelling such actions as "special treatment" to the others rather than recognising the purpose of actions as to help address past wrongs. A classic example would be opposition to additional funding for Aboriginal health and welfare measures, which are "special" in that they are not provided to all, but are properly targeted to support people with health, standard of living, life expectancy, and other outcomes that are far below the average for all Australians. This attitude is, in part, a consequence of a zero-sum game worldview that sees any gain by group X as necessarily meaning a loss for group Y; in fact, a gain for group X can produce not only positives for that group, but also flow-on consequences that benefit other groups. Standing against the racist mistreatment of non-white AFL players may curtail the freedoms of those who believe they have some right to shout whatever vile abuse that might occur to them, but it also expresses a societal view that every individual has the right to have their humanity recognised and everyone deserves to be treated respectfully. It elevates all except those who become the other by insisting on espousing racism, and in so doing, lose power. It is a context whereby the shift in majoritarian views and values serves to re-empower the victims and disempower the perpetrators.