'Opposite to' or 'opposite'?
Solution 1:
For this specific scenario, the usage of "opposite to" and "opposite" is indistinguishable in resulting meaning.
However, they cannot be used interchangeably in all cases.
"Opposite" is utilized as an adjective in:
Their house is opposite to the Red Cross Hospital.
While it is utilized as a preposition in:
Their house is opposite the Red Cross Hospital.
The divergence lies in how "opposite" as an adjective can accept an argument before it takes on the prepositional phrase headed by "to" (PP-to).
So while we can say:
The dice are opposite [in color] to the marble.
We cannot say:
*The dice are opposite [in color] the marble.
But the following statements tend to be construed in the same manner:
The rook is opposite to the knight.
The rook is opposite [in position] to the knight.
The rook is opposite the knight.
This suggests that the prepositional variant, when contrasted to the adjectival variant, is limited to having the same implied meaning as "opposite in position to". So, in conclusion, "opposite" as the head of the adjectival phrase that dominates PP-to has the potential to be applied with a greater scope.
I think that about covers it.
Solution 2:
"Opposite" is also a preposition.
So I would say :
Their house is opposite the Red Cross Hospital.