Does the UN recognize the Palestinian people as stateless? The Palestinians achieved the de facto recognition of a sovereign Palestinian state in 2012 so why are they still considered stateless?
As far as I can tell, the UN does not have a list of peoples whom it considers stateless, but the UN Refugee agency does supply a definition of "statelessness". It should first be noted that the UNHCR deals with all refugees that are not Palestinian, but as the UNRWA (which deals with Palestinian refugees) does not appear to have its own definition of statelessness, we will use the UNHCR's, which is as follows:
statelessness refers to the condition of an individual who is not considered as a national by any state.
However, this may not be a useful definition for our purposes. This definition of statelessness does not require the individual's ethnic group or nation to have a state. For example, Kurdish nationals of Iraq would not be considered stateless, but there is nevertheless no Kurdish state. Similarly, there are a number of Palestinians who are citizens of Israel or Jordan, and are therefore not stateless, but it seems that you may be asking not whether all Palestinians are stateless, but whether there is a Palestinian state.
The answer to whether there is a Palestinian state depends on what you consider a state. In 1993, Israel and the PLO agreed to the Oslo Accords. These agreements granted the Palestinians control over area comprising around half of the West Bank and Gaza. Whether you consider this area a state may be a matter of some subjectivity.
On the one hand, this area (which for the sake of clarity we will call Palestine) has a government which can grant citizenship and issue passports. It has a law enforcement agency and has a legislature, though due to a schism with Gaza and the continuing delay of elections, the legislature has been unable to meet for years.
On the other hand, Palestine does not have control over its borders, its airspace, or nearby waters, and Area B of the West Bank is under Israeli military control (though Palestinian civil control). Though Palestine is recognized as a state by the UN, it is recognized only as an observer state.
There is no absolute definition of statehood that can tell us definitively whether Palestine is a state, and therefore whether Palestinians are stateless. If Israel and Palestine agree to a final settlement that establishes a full Palestinian state, then the question may be resolved, but until then, hopefully this answer provides you with enough information to determine whether the Palestinians should or should not be considered stateless.