In theory they kinda can, or at the very least the governor has to hear them out and few people in the Imperium will say no to something like killing xenos and heretics. At the absolute worst they will see coming in and killing who they believe to be heretics as doing us a favor. Additionally an Inquisitor has a retinue to do the leg work for them in finding fracture points so they will rarely being working alone. Hell they might even have contacts in the wider Mechanicus that he can talk to about the xenos loving heretics on one of their Forge Worlds.
You seem to think an Inquisitor will just pop into our neck of the woods and announce their presence when they can very easily come to the sector without telling anyone do their investigation in secret and leave before we notice them. They're not flamboyant Rogue Traders they are the secret police and as such are expected to be skilled in things like subtlety.
Also if they do rally an army against us it is pretty much game over since a single Forge World is completely outmatched against the Imperium. We could hold out for a bit but eventually we will be worn down and defeated.
And I think you are not taking the potential consequnces of this seriously enough.
So your saying that I can counterfeit an inquisitorial rosette and just play at being king until another inquisitor calls me out. That no governor is going to call me out, and I can just do what I want and no one will ever call me on my bullshit because the chances of me encountering another legitimate inquisitor are slim to none, and even then I can just point at them and claim *they* are in fact the imposter. Especially because the compartmentalized nature of the Inquisition means that it is very likely any two given inquisitors probably dont know each other by name, or at least the possibility is high enough that they cant just say that I am not in fact, an inquisitor.
Excellent.
A governor is likely to hear out an inquisitor but unless they have proof that the Tech Priests doing their weird tech priest stuff is worth them actually sending an army, IE they got subverted by a gene stealer cult, or are opening holes into the warp, or are going to raise an army and invade the sector seeking to conquer it, those Governors arent likely going to go along with the inquisitor. Because they have their own problems to worry about. Whatever the inquisitor is doing, they still have tithes to meet and enemies to fight and their position to maintain.
An inquisitor pointing at someone and saying "Go kill those people I dont like what they are doing" isnt going to cut it. They need more substantial proof to back it up. Us being nice to the local xenos isnt going to cut it. Tech heresy DEFINITELY isnt going to cut it because a Governor wouldnt know what tech heresy looked like if it jumped up and bit them in the ass. Thats an internal AdMech concern. The Governor doesnt know what AdMech rites should look like because the AdMech run a mystery cult, outsiders need not apply.
So if your not an insider able to actually call us out, you dont have much of anything to go on. Also the Fabricator General is autocephalous, the only person who can tell our Fab Gen what to do is the Fab Gen of Mars. So local governors invading a forge world specifically to get involved in internal forge world matters that dont actually disrupt the flow of material would likely draw in other forge worlds who would want to protect their internal affairs from outside meddling. Especially from the meddling of a jumped up junior inquisitor with too much time on their hands. So in order to defend themselves from interference outside of the Cult of Mars, they would likely ride to our defense. Heretek or not heretek. As long as we pay lip service to the Cult, they are going to be on our side when it comes to outsiders butting in on our business. Because they assume that we would do the same for them were the situation reversed.
So an inquisitor, say of the Ordo Xenos would need enough proof to paint us as an actual existential threat to the local forces. They would need enough proof to convince other forge worlds in the area to not rush to our defense. Because those forge worlds autonomy is threatened by our autonomy being threatened. Thereforer they have incentive to resist a Governor supporting inquisitorial meddling. So the Governor needs to balance listening to this outsider unknown spook, versus potentially alienating not just us, but other forge worlds as well whose autonomy might be brought into question if an inquisitor can just casually mobilize the local Guard and bring a forge world they dont like to heel.
They would need at minimum the backing and support of one of the other forge worlds or the blessing of Mars itself, and that is a bridge too far for some back water colony.
To recap: They would need to convince us to turn on ourselves which I hope no one would do, or they would need the non-interference of other local forgeworlds, or the blessing of Mars itself to bring us to heel, on top of the suppport of either a local Governor or the local Imperial Guard to actually have the manpower needed to occupy our colony. Considering that we arent consorting with powers of the warp, or looking to raise an army to attack Imperial worlds, or looking to buck Imperial hierarchy at all, nor are we looking to destroy the Imperial Cult or the Cult of Mars, we just want the ability to see to our own diplomatic affairs with respect to xenos, and to our own affairs with respect to holy technology...
This threat isnt one. Not that an inquisitor wouldnt disapprove, but I doubt their ability to actually be able to do anything about us. At least not until an actual legitimate problem pops up somewhere else to take away their attention.