First, Mr. Trumbull was speaking in regard to the “wild Indians†- that is, members of tribes that lived within the territories, but outside of any state. Second, Mr. Trumbull did not define allegiance. So it is only reasonable to proceed on the basis that he would have agreed with the long-standing doctrines of allegiance that then existed. Under these doctrines, as summarized in great detail in US v. Wong Kim Ark, 169 U.S. 649 (1898), allegiance was owed at all times by an individual to the sovereign who had control over the territory where that individual was present at the time - allegiance meaning in essence the obligation to follow all of the laws of that sovereign - unless some recognized exception applied. As set out in the Wong Kim Ark case, ambassadors were, as a matter of ancient custom and international law, granted immunity from local law when they were officially present in a foreign country because the allegiance the ambassador would otherwise have owed to the sovereign of that foreign country would have been antithetical to the interests of the sovereign who sent the ambassador overseas in the first place. See p. 685.
The reason why multiple allegiance was an issue with the “wild Indians†and other recognized Indian tribes was that, because the US had recognized the tribes as being quasi-sovereigns, a member of a tribe who was present within the lands controlled by that tribe would owe allegiance to that tribe based on presence and was therefore not fully subject to allegiance to the US, despite the fact that the US also otherwise exercised aspects of sovereignty over the same territory.
Put into context, it becomes clear that the issue was whether there was some overriding immunity that a person possessed on account of his relationship with one sovereign that prevented him from owing complete allegiance to the sovereign who controlled the territory where the individual currently resided.
In the case of “wild Indians†and foreign ambassadors, there clearly is an immunity, based on a relationship to another sovereign, that the US recognizes as such, and which allows such an individual to avoid having to obey all the laws of the sovereign who governs the territory where he resides.
In the case of temporary sojourners or ordinary visitors, no such immunity exists, and those persons owe allegiance to the sovereign who controls the territory they are visiting, in the sense that they are obligated to obey all of that sovereign’s laws without exception, and can be prosecuted for failing to do so.
That is the case with your average foreigner who enters the US, whether legally or not: he or she is required to follow all of the laws of the US and of the state in which they are present, without exception, and can be prosecuted for failing to obey. That is, they owe full allegiance to the US when they are physically present in the US.
Thus, when put in context, Sen. Trumbull’s remark does not support the proposition for which it is being cited here. That is, it does not undercut the fact that the 14th amendment granted birthplace citizenship to everyone other than a select few people.