Mages - Returned to the Towers. Rebel mages who refuse to bend the knee will die or be made tranquil.
Templars - Returned to their role of protecting the mages. Templars who go beyond their mandate to both protect mages and society, and instead abuse their charges, will die.
Elven rebels - The Inquisitor will sympathize with the plight of the elves, and should any in positions of power ask his opinion, he'll voice support for an end to the alienages and the elves gaining equal treatment under the law. Elves who seek to enact change however through violent means like rebellion, will have signed their own death warrants. Revolts will be crushed mercilessly and anyone who sows chaos and disorder in the realm can expect no quarter.
Dalish Elves - This depends on what the clan(s) encountered are up to. If they are minding their own business he'll have no problem with them, and would defend them against humans infringing on their rights. If they are involved in attacks on humans they'll be crushed.
Seekers - Unsure. I assume they are going to be part of the Inquisition, but I guess we'll have to wait and see.
The Chantry - The Inquisitor will be secular rather than pious and question whether the Maker exists (agnostic), but he'll support the role the Chantry plays in helping to maintain some order in society in Thedas. He won't be seeking to tear down the Chantry or radically alter society.
Orlesian Loyalists - Unless the plot forces the Inquisitor and Celene into opposition, he'll pledge an oath of loyalty to her. She is the rightful ruler of Orlais. Her enemies will be his enemies.
Orlesian Patriots: Gaspard is a traitor to the realm and and for that he must die.
Grey Wardens: Unsure. I'll say neutral for right now, but that depends on what they are up to in DA:I.
Tevinter: Unsure. Neutral also for right now, but it also depends on what the nation is up to in DA:I. The Inquisitor will mildly disprove of Tevinter's political system, where mages not only exist outside the towers but rule.
Qunari: They are a threat to all of Thedas. Unless their goals happen to align with the Inquisitor's, he'll seek to undermine them at every opportunity. He'll view the Qun and its caste system with scorn and will not be diplomatic about it when conversing with Qunari.
Ferelden - Unsure. It depends on whether or not the Inquisitor is from Ferelden, Orlais, whether he has pledged allegiance to Celene, and what the nation of Ferelden is up to in DA:I.
Antivan Crows: He'll view assassins as murderous scum whose loyalty can be bought by the highest bidder, but he'll also view them as a potentially useful tool. He wouldn't hesitate to employ assassins to eliminate rivals or enemies who threaten the security of the realm, even though he may view assassins with private disdain.