Galicia was not part of the Kingdom of Hungary, the habsburgs favored polonization there (okay, its not entirely true, because the dinasty did not liked any kind of natinalism, it was mostly a religion thing, favoring chatolicism. Something along the lines wih the ruthenes with the greek catholic church...)
If there would be a clear Magyarization program, from 67, by 1914 the clear majority of the Kingdom of Hungary (minus Croatia) would have been considered himself as hungarian. There were no such program, strings of individual efforts, sometimes even from ill-interpreted and misguided goodwill (the worst of its kind).
But i still think, that even that did not mattered - the ruling upper class was the biggest problem, along with the immense amount of poverty.
Ok, you want the Kingdom of Hungary only. There was a clear Magyarization over the time period you want (1867-1914), but it was weak. We see some clear recruitment of non-Hungarians to Hungarians. A bit of a stereotype but illustrating, a rural extended family of Romanians moves to an urban area around 1970. Two generations later, 2 of your 8 grandchildren view themselves as Hungarians, or at least use Hungarians as their first language. The Hungarians also did it through the visa to leave process. There were a lot more small barriers to leaving the country.
Some readings I have seen indicate that the outreach efforts towards Jews in Hungary had gotten many of them of to view themselves as Hungarians first for nationality, who was also in the Jewish community. Avoid the horrors of WW1, and these people probably largely support the Hungarian status quo in civil war, at least as much as non-noble Hungarian.
Now it has been a year since I looked at the numbers and this is from memory. If highly important, you can look up the details, but it generally went like this one.
In 1867, the Hungarians were 46% percent of the population. They were more urban so had lower birth rate, so if nothing else changes we would expect to see about 42% Hungarian. But we see 50-52%. So it was success from some perspective. The Hungarians were well on their way to achieving a durable majority, if given a few more generations. They were gaining up to 10% growth rate on base. Now from another perspective, they were failing. It was taking generations to reach a clear supermajority. It made the minorities mad, which in many ways would give the Germans Austrians a way to suppress the Hungarian nobility. (Not clear to me the average Hungarian actually cared that much about extra autonomy to some Romanian village in the mountains.) And it was so slow, there is a big risk over another few generations, the Hungarians would need to lose some land or give up some autonomy to some minorities. A good example of the down side is that Croatian troops were tasked to taking the Hungarian capital in the civil war orders issue then recalled IOTL. The anger of the Croatians at Hungary made them more reliable troops in a civil war than Austrian Germans.
And this is where I think they were generally heading. Look at some of the proposals floating around. The final solution is probably within the bounds of what was proposed by various bodies.
- Triple Crown: Remove large number of Serbs.
- United States of Austria - Remove most minorities.
- Remove Germans in what is now Central Romania from Hungary to Austria, along with few other enclaves.
Or put another way. A defacto smaller area under Hungarian Magyrization. You get a area with clear super majority of Hungarians (over 2/3) with few to no large areas less than 50% Hungarians. The key on unity becomes not so much demographics since Germans will never be 50% of all of A-H, but can the Austrians make it appear better to be "Hapsburgish" and for Hungary to live in the A-H system than Hungary be a client state of the Tsar. I lean towards A-H surviving, but having some very awkward compromise absent WW1 or another Great War.
Note: The census and estimates are biased and have a human thumb on them, you can see the underlying pattern. Also, don't get too worked up on individual numbers. The underlying trends are what was happening. When you dive into details of estimates in Austria and Hungary and Poland, we see everyone of the day had an agenda.