What does it mean to awaken or become self-realized? Is this an objective state of consciousness? What does it mean to fully realize the non-dual nature of reality? Can we deny these ideas when they have been so thoroughly mapped and realized by so many thousands over so many centuries?
Enlightenment has lots of definitions in different traditions. In Buddhism, it is not a state of mind. It is not something you gain. It is not a wonderful experience of light. It means that fetters/chains that bind us to the world of suffering are broken. In the oldest texts there is a four stage model. Sotapanna (stream enterer), sakadagami (once-returner), anagami (non-returner) and arahant (one who is worthy). All four could be referred to as enlightened, but the body/mind has not been completely brought in line with the realization before stage 4.
The fundamental realization is seeing through the illusion of self/other, me & mine. This is not merely an intellectual understanding that there is no seer of the seen, thinker of the thought, feeler of the felt, hearer of the heard etc... It means that you have seen the self for what it is, and even feelings of self (such as identifying with thoughts, feelings in the chest, pressures inside the head etc...) are no longer felt as being "me", in the sense of an inherently existing entity. It doesn't mean a mental illness where such things go away (like schizophrenia), but rather the identifying with such mental phenomena as self ceases permanently.
This creates a strange problem when it comes to talking about being enlightened. From the point of view of someone who has not become enlightened, there is such a thing as becoming enlightened. From the point of view of the one who has, there never was, is not and never will be any inherently existing entity that could become enlightened, and so someone whom this has happened to will not go around proclaiming "I am enlightened". That would be deeply contradictory to the nature of the realization. If such language is used, it must be out of compassion. When seeing someone struggling with believing there is such a thing, or thinking that it could never happen to them because they are "unworthy" or because we live in a spiritually "degenerate" age, someone enlightened might be moved to tell someone that it is possible, it happened to him or her, in order to help the other along the path.
Are there enlightened people today? There sure are. Quite many, from a variety of religious traditions (and sometimes no religious traditions at all). Are there fully enlightened people who are completely perfected in the realization? I don't know for sure, but I see no reason why there would not be.