Are inter-caste marriages allowed in Islam?
There is no caste system in Islam so there is no question of "not being allowed to marry someone from a different caste".
In India, Muslims have what you can call as families or Biradaris where for some who trace their lineage to the Prophet's family are called as Syed, those who come from Abu Bakr's family are called Siddqui, those from Umar's family are called Farooqui, those from Usman's family are called Usmani etc while combined together they are called Shaikhs etc.
What has to be stressed here is that the existence of these families or biradaris does not mean in anyway that one is lesser than the others just because of their birth. This is a social and a cultural construct which does not have any basis in Islam.
In the Quran, Allah says:
O humanity! Indeed, We created you from a male and a female, and made you into peoples and tribes so that you may ˹get to˺ know one another. Surely the most noble of you in the sight of Allah is the most righteous among you. Allah is truly All-Knowing, All-Aware. Quran 49:13
Allah first states that everyone comes from the same set of parents so there should be no thought of someone being better than the other just because of their birth. Then Allah states that He has divided humanity into people so that we can love and know each other. Not to fight and denigrate each other.
The Prophet in his last sermon clearly said that:
O people! Your God is one and your forefather (Adam) is one. An Arab is not better than a non-Arab and a non-Arab is not better than an Arab, and a white person is not better than a black person and a black person is not better than a white person, except in piety.
In the end, Allah knows best. I hope this helps.