How did the Roman military become composed of almost all non-Romans with questionable loyalty to Italy?

Already during the Principate, Barbarians were offered posts in Roman army, often leading auxiliary or irregular troops. Imperial army included up to half auxiliary troops in its misdt. What changed in the Third Century, is not that Barbarian recruitment was suddenly more important numerically, but that it became synonymous with readily available high-quality troops.

The Third Century Crisis is a complex set of events : since the late IInd century, a renewed pressure on eastern imperial borders (furthermore increased with the Sassanian dynasty) forced a gradual strategic refocus there, both financial and operational. Barbarian raiding and piracy, which were more or less regularily happening on the limes already, found there an opportunity.

These Barbarians, often but not systematically Germanic (even within a same people), already had various relationship with Romans since the latter advanced up North. Trade, seasonal cross-border work, military service, subsides given to client chiefs (traces of Roman presence, probably advisors, were found as far as Poland); but also raiding, counter-raiding, etc. made the "inner" Barbaricum part of the wider Roman cultural an political sphere, the border regions getting developed (with, notably, traces of pastoral and agricultural developments) and attractive to "outer" Barbarian groups (Eastern Germanic, Sarmatians, proto-Balto-Slavs, etc.) whom several groups underwent migrations towards the Roman limes, although less as coherent and politically defined group than slow familial migrations along rivers and trade-ways.

Subsides (paying the peace or the alliance) to Barbarians were nothing new at all in the late Roman Empire, and actually represented the capacity of the Empire to increase its political reach on people living beyond its borders; with a marked efficiency.

Organizing in local alliances (Goths, Franks, Alamans, Picts, etc. not really existing beforehand but being likely a consequence of settlement and development along the Roman border of various, indigenous or not, peoples), their raids became more organized and important, on a Roman Empire that suffered from being under Persian pressure already, had as well to deal with other issues such as civil wars, climate change (which did impact on an intensive agricultural model built on grain and mercantile production), starvation issues, etc.

These attacks might not have been systematically successful, but significantly aggravated the situation in european provinces, would it be only by their budgetary cost for an empire whom fiscal income was damaged, but more generally on all the other factors mentioned : precarious security meant less production, which was essentially agricultural, less food a demographic decline (starvation, epidemics, lower birthrate or infant survival, etc.), which itself meant lower fiscal income, then budgetary issues, inability to pay troops, increased attacks, provincial revolts (either fiscal, or as in Gaul, in order to use Gallic income to protect Gaul first), which requires troops to defeat while borders are still insecure, etc.

The same Barbarians, however, provided a solution : emperors would make a great display, not only defeating Barbarians, but "importing" them as either rural workforce or military specialist troops to make due with a less important Roman recruitment (maybe less because of "civic decline" than because it was less attractive financially). And it worked fine for most of the IVth century. Barbarian being settled in the empire (either as scattered groups, either as communities) and serving as a safe military recruitment pool (and considered of higher quality than Roman humiliores conscripts), the borders held, allowing the Roman state to reinforce itself.Now, it didn't stop civil wars to happen, but these weren't really a new occurrence in Roman history : that Barbarians made up an important (altough nowhere exclusive) part of them didn't changed this. At the contrary, this state reinforcement provided several opportunities for settled Barbarians to raise in late imperial hierachy : Frankish officers as Bonitus, Ricomer or Merobaud became generalissimos, consuls, etc. without anyone really complaining. Some, as Silvanus, rebelled but not as much as Franks than as Roman generals, and generally adopting the same behavior than, say, a Carausius.

In fact, these Barbarians only got more romanized with time, adopting Roman cultural features (both materially and immaterially) and while keeping sort of double identity (Roman soldier, Barbarian citizen) which was already something in the early IInd century and aware of their political identity (Barbarians were usually not citizens, but under direct imperial patronage, implying that imperial successions or coups represented either status precarity or opportunity) were neither more or less loyal than Roman armies or communities. In fact, the promotion of Barbarians in an imperial military administration could even underscore the perception of a greater direct loyalty of Barbarians to the emperors, rather than from an Roman elite pool that demonstrated its capacity to revolt and pretend to the purple multiple times; some of these groups, e.g. Franks or Alans, actually proved their overall loyalty during the troubles of the Vth century; and highlighting this direct relationship, when Barbarian converted to Christianity in the IVth century, they did adopted the emperor's credo : Homoianism was originally adopted by Goths as emperors were so, then Burgundians adopted a Nicean credo because it ceased to be the case.

From the early to the late IVth century, relations with Barbarians were thus already appeased : migrants and raiders still presented themselves at the border, but were eventually managed, defeated and generally integrated within the Late Empire, up to become citizens for several of them : Stilicho, in spite of his non-Roman origins, didn't went trough agreement with Barbarians because of it, but because he basically followed the traditional Roman policy on Barbarians, never displaying himself otherwise than a Roman high-public servant, his origins being more a perceived problem for palatial coteries . Basically, Barbarians within the Late Roman Empire could be considered as "hypenated-Romans" of sorts, distinguished by their origins and their communal militarization.

Now, while integrated and roughly loyal to the idea of the empire Roman were, it didn't meant Barbarians were push-overs or didn't took care of their own interests as communities. When crossing the Danube in 376 in exchange of a protected status, christian Greutingi Goths were shamelessly scammed and threatened to see part of their people enslaved, as they didn't took it well and eventually defeated a Roman counter-insurgent army, they were able to renegotiate their status within the empire, still under a double identity of Roman army and Barbarian people. It's important to understand that Barbarian identities were less based on culture or language (apart from peripheral groups, all important Barbarian languages fell into disuse as late as the VIth century) but on a political identity : whoever followed a Barbarian king was reputed being a Barbarian, rather than a Roman citizen; and thus, a lot of Romans (as slaves, but also as fiscal refugees, deserters, or armies corps wiling to benefit from a status upgrade) were to be found in Barbarian armies; making the cultural distinction further confuse.

The problem of the Vth century wasn't that Barbarians in particular weren't loyal to Rome, but that integrated within Roman political and institutional frames, they became part of its political conflicts, and for the most part, took over a post-imperial society; not as "foreign" elements but as distinct political elements in an era of warlordsism.