Under the Yuan Dynasty, although the Mongols were the most privileged group politically, they were not the dominant group demographically. In fact, Mongols were an extremely tiny minority in Yuan China. It's essentially impossible for <1% of the population to assimilate the rest - they're way more likely to be assimilated into the majority.
As such, it would've been more reasonable to assume that Mongols outlawed intermarriage in order to protect their cultural identity from being assimilated. However, that is not the case.
There's no evidence that Chinese/Mongolian intermarriage was forbidden.
Even though the idea of a ban gets repeated a lot, it is flatly contradicted by the historical record. Among royalty for example, Zhenjin's second son Darmabala is known to have married a Chinese woman with the surname Kuo. Intermarriage was even more common among lower class Mongolians. A study of Imperial Examination graduates found, staggeringly, that:
Among Mongolian jinshi, 68.2% had Chinese mothers; 71.4% married Chinese wives.
Hsiao Ch’i-ch’ing, "Backgrounds of the Mongol and Se-mu Chin-shih
of the Yuan Dynasty: An Analysis". Chinese Studies, 18(1) 2000.
In fact, provisions exist in Yuan China's legal code, specifically to protect Mongolians in the case of intermarriage:
[I]f there were ambiguities in the application of law in a case of intermarriage, the disputes were to be adjudicated according to the husband's law. if the wife was a Mongol, however, the disputes automatically were to be decided by Mongolian law. Consequently, Mongolian law prevailed where a party to the intermarriage was a Mongol, be the person husband or wife.
Ch'En, Paul Heng-Chao. Chinese Legal Tradition under the Mongols: the code of 1291 as reconstructed. Princeton University Press, 2015.
This wasn't a later reform either. As early as in 1271, the year Kublai Khan proclaimed the Yuan Empire and promulgated a new legal code (replacing the previous Jin and Song laws):
1271 February, Imperial Decree: Each race who marry their own kind should follow their own customary laws. Those who intermarriage, should follow the husband's law, except for Mongolians.
The Great Yuan Legal Compendium
Likewise, many Han Chinese studied the Mongolian language under Yuan China as a way of currying favour with Monglian nobility. The only reference I could find of any language ban dates to the premiership of Bayan, a nationalistic conservative who came to power in 1337. He proposed many policies to suppress the Chinese population, including a massive purge based solely on surnames.
However, Bayan was toppled by 1340 and his policies reversed. Thus, the idea of any language learning ban - if it was indeed implemented - is overstated.