Was it ideological appeal among some sections of the rank and file of of the Russian military? Or was it promises of high positions to the higher-ups? Was it both? Something else entirely?
Peace, Bread and Land! All Power to the Soviets!
Support for the Bolshevik revolution by the military class can be distilled down to two central issues:
The first issue here is that the First World War was going just awfully for the Russian Empire almost from the start. This created a front that was increasingly war weary in the physical sense and a rear that was increasingly war weary in the moral sense. Such conditions gave the Bolsheviks the opportunity to undermine the military leadership of the Russian Imperial Army and redirect those soldiers who had abandoned the front already, or were considering abandoning the front, by providing the motivation they needed to join Red Guard formations in Saint-Petersburg (then called Petrograd) and participate in the revolution, while it gave discontent factory workers and peasants an actionable outlet beyond peaceful protests (which were increasingly put down with force) to express and manifest their desire to overthrow the imperial government whether through participation in the Red Guards or participation in local Soviets, or councils.
The second issue was the order mentioned above which took advantage of the aforementioned discontent and catalyzed the process of reassigning authority in the armed forces. Ostensibly this was a "democratization" of the armed forces so the soldiers themselves were in control, but realistically, the goal of the order was simply to undercut the established military order and reconstitute it underneath the authority of the Petrograd Soviet.
The Material Failings of the War
Let's look at two descriptions of World War I from the perspective of the Russian Empire. The first is from Lev Trotksy's History of the Russian Revolution (1932):
"Russia's participation in the war was self-contradictory both in motives and in aims. That bloody struggle was waged essentially for world domination. In this sense it was beyond Russia’s scope. The war aims of Russia herself (the Turkish Straits, Galicia, Armenia) were provincial in character, and to be decided only incidentally according to the degree in which they answered the interests of the principal contestants." (text of the chapter)
The second from Professor Dominic Lievan's Towards the Flame: Empire, War and the End of Tsarist Russia (2015):
"For the Russian people the greatest tragedy was that the two million soldiers who died in Russia's First World War died for nothing. In large part because the Revolution meant that Russia was not one of the victors at Versailles, the first world war needed to be fought a second time at terrible cost 20 years later." (pp. 28)
The former of these is obviously severely propagandized considering its author was among the instigators of the October Revolution, but provided alongside the latter, it shows how effective similar propaganda was given the complete lack of understanding by the average person of Russian participation in the First World War. The true causes of World War I are quite convoluted in and of themselves as well; this answer by u/DuxBelisarius from the FAQ covers those issues at length; any military historian will tell you that costly wars fought for ambiguous political end states do not for a good time make.
The eastern front is illustrated quite nicely by this map which shows the war at several crucial junctions, most importantly to your question, the dotted black line labeled Farthest Russian Advance 1914 and the bold yellow line labeled Front at the Time of the Russian Revolution 1917. The eastern front moved significantly westward, consuming most of Galicia and East Prussia, and even crossing the mighty Vistula River for a time. This advance was the result of the initial Russian offensive in 1914:
The Russian Imperial Army suffered somewhere between 5 and 7 million total casualties^([)^(1)^(]) during the entire conflict which lasted for 4 years of fighting, but this initial offensive, which finally had to be halted because it was the middle of winter, resulted in nearly 700,000 casualties (between 10% and 14% of the total) in the first four months of the war. The only gains the empire really made were at the outset of the war itself, and they came at absolutely tremendous cost. Suffice to say, as the front was pushed further and further back towards Russia proper, and more and more life was lost, the war effort (at the helm of which was Emperor Nikolai II himself remember) grew more and more unpopular.
Lievan sums up just how blindly the Russian government stumbled into the First World War:
"Exciting the Russian masses about Constantinople or their Slav brothers proved an impossible task. In 1909, Grigorii Trubetskoy’s brother Prince Evgenii Trubetskoy wrote that only someone who believed Russia to be a 'corpse' could imagine that when it stood up for its honour and the Slav cause against Germany, there would not be a surge of 'powerful and elemental patriotism.'
The First World War was to prove him wrong." (pp. 131)
Order No. 1
When the people had finally had enough and the February Revolution occurred between 8 and 16 March, 1917 the Emperor returned to Saint-Petersburg, abdicated and a Provisional Government was formed in Saint-Petersburg to rule over Russia. This Provisional Government importantly had two branches: the State Duma and the Petrograd Soviet. The former of these had existed since 1905 when earlier protests against imperial power had compelled Nikolai II to create some kind of legislative body that was nominally answerable to the people, but the later was formed during the February lead-up to the revolution itself by revolutionary socialists, among them, those austere gentlemen who would come to be known as the Bolsheviks. Just a side note here, the Russian Empire still used the Julian calendar which is about a month off from the Gregorian calendar (the one used nearly the world over today), so those dates I mentioned above occurred in February O.S. (old style), thus the name. But I digress.
The Petrograd Soviet is described by Trotsky:
"The twofold government of the liberals and the democrats only reflected the still concealed double sovereignty of the bourgeoisie and the proletariat. When the Bolsheviks displace the Compromisers at the head of the Soviet-- and this will happen within a few months-- then that concealed double sovereignty will come to the surface, and this will be the eve of the October revolution. [...]
[F]or every two worker-delegates in the Soviet, there were five soldiers. The rules of representation were extremely elastic, and they were always stretched to the advantage of the soldiers. Whereas the workers elected only one delegate for every thousand, the most petty military unit would frequently send two. The grey army cloth became the general ground tone of the Soviet." (text of the chapter, see also Chapter 12: The Executive Committee)
Compare this to its polar opposite, the Russian Imperial Ministry of Foreign Affairs (largely responsible for bungling the empire into the war in the first place) as described by Lievan:
"[T]he Foreign Ministry... [was] a nest of the aristocracy and gentry. The nest was very, very small: in 1914, there were fewer than two hundred men of all ages who had passed the diplomatic exam and in principle were eligible for mainstream posts." (p. 119)
We're starting to see the answer of your question here, but not the exact cause of why so many soldiers flocked to the banners of the Petrograd Soviet, and here's where Order No. 1 comes into play. The disregard for the common soldier is shown above, so we can understand exactly how they must have felt disregarded, disrespected, and generally disdained by their own leadership but how were the Bolsheviks able to attract such large numbers of them to the Petrograd Soviet to accept new orders?