The answer is, in broad terms, basically pretty simple: while Mongolia and Tibet both became de facto independent, by the time the CCP came to power in 1949 the former had become a socialist satellite state of the USSR while the latter remained a semi-independent entity over which the CCP could still claim to have sovereignty, and so a reconquest of the latter was possible but not of the former.

But this is a bit of an unsatisfactorily brief thing to say, so I'd like to offer an alternative viewpoint for the question, so we can think about this in a different way. Instead of thinking of Mongolia and Tibet as declaring independence from China, why not think of China as declaring independence from Manchuria, such that Mongolia and Tibet essentially resumed as normal, just without Manchu oversight? It's an odd statement, to be sure, but I think it's important to get us away from a model of the Qing that sees it as always having been 'China + peripheries' and toward a more multipolar view, where the Qing empire consisted of six unequal and interrelated, but nevertheless distinct regions: Manchuria, Mongolia, China, Taiwan, Tibet and Turkestan. Over the course of the dynasty, the methods of management of these territories underwent significant change, culminating in the developments of 1911-12. In turn, it challenges us to ask a somewhat different additional question: why was the new republic able to inherit Manchuria and Turkestan from the Qing, but not Mongolia or Tibet?

Essentially, Manchu rule in the Qing empire was never a matter of simple imposition. Rather, the Manchus retained local administrative structures and cooperated with local elites, with the insertion of Manchu officials and military forces to oversee the process. Looking at the state of the empire around the turn of the nineteenth century, this insertion could be more or less intrusiive depending on the region. Manchuria goes without saying as a region nominally administered entirely by Manchus (I'll get to the 'nominally' bit in a moment.) In China, the military presence was comparatively limited outside major hub cities and the frontiers, but officialdom was massively disproportionately Manchu – as late as 1911, 6% of bottom-level district magistrates were Manchus, compared to 1% of the population at large, an overrepresentation that only increased as you went up due to favouring of Manchus over Han Chinese for promotion. In Turkestan, the military presence was much more pervasive, with a garrison in every major city, but civil administration was largely cooperative, conducted through hakim begs for each city, who often maintained their own staff of sub-begs for specific duties. Tibet was even more loose-rein, with the existing administration in Tibet proper being essentially maintained in its entirety, including tax autonomy, with the only major imposition being Manchu ambans, most prominently at Lhasa, who could and did exercise a range of extraordinary powers, but did not have a major role in regular administration. Mongolia was a little more stratified, with comparatively tight control in Inner Mongolia and looser control in Outer Mongolia, but both essentially were maintained through arrangements with tribal heads called jasaks, who ruled groups of Mongols known as khoshuns, or 'banners', with the amban at Ulaanbaatar and the military governor of Uliassutai having jurisdictional authority over the eastern and western parts of Mongolia, respectively. Fortified garrisons, dispersed throughout the region, served to delineate areas of pasturage. Finally, Taiwan, although part of the Chinese province of Fujian, was not exactly run in typical provincial fashion. The Han Chinese population was, until the latter part of the nineteenth century, largely constrained to a few areas of agricultural colonisation on the island's west coast, which had already been established by the post-Ming regime that ruled the island until 1683, while the Qing maintained particular arrangements with aboriginal leaders in the hinterlands.

The extent to which Chinese personnel were drawn on to administer these regions varied. The three Manchurian provinces of Fengtian, Heilongjiang and Jilin (a.k.a. Mukden, Sahaliyan ula and Girin ula) were run from the city of Mukden (Shenyang) by Manchu officials, but Han Chinese officials were responsible for administering fellow Chinese migrants; China, as we have said, maintained its existing bureaucracy but with an overrepresented Manchu component; by extension Taiwan obviously fell under the Chinese bureacuracy as well; said bureaucracy had a number of administrative posts in Turkestan, which were often used as punitive assignments for officials in China proper; and Tibet and Mongolia were largely Han-free by virtue of their administrations being run largely through Manchu bodies independent of the Chinese system.

Over time, however, large parts of the Qing empire were essentially usurped by the Han Chinese. Over the course of the nineteenth century, the administration of the Qing empire became increasingly Han, with the main accelerator being a series of wars in the mid-late 19th century that, due to being fought largely using Han Chinese provincial militias, prompted significant concessions to Han Chinese gentry and officials. I'll deal with the exception first: Manchuria's integration into the Chinese system was the product of large-scale migration, which eventually led to the population becoming overwhelmingly majority ethnic Han, leading the officials responsible for Han affairs to therefore have an increasing role in the provinces' general government. The erosion of Manchu power in China, however, can to a great extent be attributed to the mid-century military crisis caused by the Taiping uprising. The 14-year civil war against the Taiping saw the establishment of provincial militia armies led by scholar-gentry officials, administered through private bureaucracies and funded through taxes whose collection was devolved to and collected at the discretion of those officials and their staffs. The post-Taiping order in China was one in which officialdom was much more Han-dominated, with Han provincial governors beginning to outnumber Manchus, and the crucial business of local administration largely falling into the hands of bureaucrat-gentry cliiques. In turn, these militia armies would be vital to the wars that would then be fought in Turkestan and Taiwan. Han officials and generals, most notably Zuo Zongtang, pushed for a reconquest of the three marches of Xinjiang from Yaq'ub Beg's Emirate of Kashgar, which had ruled the region since 1865, and after said reconquest Zuo's army would play an important role in the military standoff with Russia known as the Ili Crisis, so named because of the Russian seizure of Ili and Almaty during Yaq'ub Beg's rule that the Qing were contesting. The importance of the Han role in maintaining the region was clearly recognised, and the Qing bowed to further Han pressure when they made Xinjiang a full province under the Chinese system in 1884, run by a Han governor. That same year, France invaded Taiwan as part of the Sino-French War over French expansion in Viet Nam, and the success of Chinese troops in pinning down the invaders in Keelung would in turn see Taiwan made a separate province in 1885. However, no such processes occurred in Mongolia or Tibet, neither of which was significantly threatened by external forces save for a brief and largely unsuccessful Nepalese invasion of the latter in 1855-6.

As such, when the Chinese overthrew the Manchus in 1911, a number of territories formerly ruled by bilateral Manchu-local arrangements had since become integrated into the bureaucratic system previously constrained to China, itself now increasingly operated by Han Chinese. When China revolted in 1911 and forced the abdication of the Qing, three of the five regions making up the Qing empire had since been essentially subsumed into the Chinese administration (Taiwan having been annexed by Japan in 1895), and although the former empire would soon disintegrate into warlord feuding, said warlords would be broadly Han, even those in Turkestan (including the Soviet-sponsored Sheng Shicai in the 1930s). The new republic was also nominally able to exercise a degree of control over Inner Mongolia thanks to it already having been a rather more integrated territory. Outer Mongolia and Tibet, however, which were always relatively autonomous, essentially did not so much achieve independence so much as lose their overlords to the Chinese revolt, and were able, essentially by virtue of the Chinese republic's disunity, to avoid being reconquered.