According to Chakotays' collar insignia he is a Lt. Commander by commission. In this case a field commission. But if Star Trek is true to staying in line with this overt exhibition of Chakotays' collar rank, I believe there is another explanation rather than the Star Trek producers made a blooper and now they're keeping their fingers crossed and hoping no one will notice. I believe the Star Trek production heads have very well informed people working for them. There is a whole crew of people who's only job is to look for the details. So I'm inclined to think Cakotays' insignia was by design. True, even the best people make mistakes, but I don't think a mistake was made in this case. Here's why;
In the regular military, whether Army, Navy etc, there is a common practice referred to as "positional authority". Which basically means in most cases regardless of ones rank, the individual is addressed as their positional title holds. (sometimes this doesn't apply to enlisted ranks depending on situation)
For example; when an officer holding the rank of lieutenant commander captains or skippers a small vessel, he is referred to as Captain or more accurately "the captain of the boat". But no one would ever address them as Lt. Commander unless talking to someone else in a third party description and in that case they would still more likely describe them as "the captain of the boat". In face to face situations they would simply address them as Captain or Skipper. If the person was enlisted they would be called Chief or Chief of the boat. In Chakotays' case, he is addressed as Commander or First Officer (never Lt. Commander).
There are many other examples of this in the regular military, especially the Navy (which is what Star Treks ranks are modeled after). Chakotay is in fact a Lt. Commander. But because of his "positional authority" as Executive Officer/First Officer he would never be addressed as Lt. Commander.
Whereas the examples of Data and Geordie you will notice they are addressed interchangeably as Lt. Commander or Commander depending on circumstance. They have no "executive position" other than being senior officers or department heads. But this does not apply to Chakotay because of his position as Executive Officer/First Officer..
It also works the same in reverse. If, for example, a higher ranking officer such as an Admiral is still permanently assigned as Captain, the Admirals "positional authority" applies as Captain if he has not been properly relieved from this "permanent assignment". Though typically once promoted from a Captain, Admirals rarely switch between assignments. Admiral Pike, for example, is not addressed as Admiral when he is on Enterprise because his assignment is still technically permanent until he is properly relieved (another person replaces Pike and is given the command permanently). In this case Pike had not yet been fully relieved of his duties as Captain. In fact, he changes uniform to the rank of Captain when on board Enterprise because he had not yet been relieved of that position. Why is this? Because technically a flag rank such as an Admiral can not have "permanent assignment" command of a ship. Only in much rarer cases such as "temporary assignment", can a flag rank command a ship. More to the point flag ranks are designated to command fleets of ships, not one. Whereas Captains are typically designated to command "one ship". This is what is know as designated billets or billet assignments. Are the so called rules broken on occasion? Sure they are, but usually under extreme circumstance. But these circumstances are not the rule or the norm.
When command of a ship is in a transition period, like the example of Pike, it is an accepted practice for Admirals to switch back and forth from Captain to Admiral. But this is not the case of "temporary assignment". For example; when waiting to replace a person to be "permanently assigned" as Captain of a ship, such as the case with Pike. He technically held both positions as Admiral and Captain. But when he was on the Enterprise he was Captain because he was still "permanently assigned" as Captain. However, there are situations where an Admiral would "temporarily" assume command of a ship in which case he would still be addressed as Admiral. This happens often and in different ways in the Star Trek series.
An example of "temporary assignment" was when Admiral Kirk was assigned to Captain the Enterprise. On each occasion you will notice that his assignments to Captain the ship where "temporary assignments". Therefore his Admiral rank was kept intact. But unlike the Pike situation, there was already a permanent replacement to Skipper or Captain the Enterprise (Captain Decker). Notice Decker was temporarily reduced in rank to accommodate his new temporary "positional authority" as Executive Officer/First Officer. With officers ranking from Ensign (O-1) up through Captain (O-6), a temporary demotion in rank is acceptable for "temporary assignments". But this demotion in rank would not apply to flag ranked officers that take on a "temporary assignments". Flag rank officers are basically everything above a Captain in the Navy or a full bird Colonel in the other military branches respectively. (commodores, admirals, generals),. The only situation which I'm aware of where a flag rank officer can be reduced in rank is in the situation I described with Admiral Pike. Also, you will notice later in the Star Trek motion picture series Kirk was busted down to Captain when Star Fleet wanted to "permanently" assign him to Captain the new Enterprise. They had to bust him because there was no other way to reduce him to Captain. Star Fleet could not "permanently assign" an Admiral to captain a ship.
Anyway, in the case of Chakotay, he was field commissioned at the rank of Lt. Commander but was basically double field commissioned as the First Office/Executive Officer or Second in Command. This makes him technically the senior officer on board because of his "positional authority" as First Officer. Even if there were other full Commanders or Captains on board besides Janeway, because of Chakotays' "positional authority" he would supersede all other officers regardless of their rank except Captain Janeway. Yes, Chakotay would extend any and all courtesies to these other Captains and full Commanders if they were on the ship, but when it comes to ship business and having the last word, the Executive Officer/First Officer could not be overridden by these other Captains or full Commanders unless said people where given orders to override from the Fleet Command.
I hope this helps.