A language is context-free only when it has only one condition in the formation of language.
For example $ L_1 = \{ a^n b^n | n>= 0 \} $
A regular language, will not have any conditions.
For example $ L_2 = {(a + b)}^* $
So Intersection, of condition and non condition will return that one condition,
Hence $ L_1 \cap L_2 = L_1 = \{ a^n b^n | n>= 0 \} $ Hence, Context free.