Kate asked me if I liked(like) watching movies?

[keannu]

For your general preference in past questions, can you also say the present tense? I think it's possible.

ex)Kate asked me if I liked(like) watching movies.

[Raymott]

For your general preference in past questions, can you also say the present tense? I think it's possible.

ex)Kate asked me if I liked(like) watching movies.

It's better to adopt the practice of always backshifting - this is always acceptable, whereas using the present tense is not always suitable.

[5jj]

For your general preference in past questions, can you also say the present tense? I think it's possible.

ex)Kate asked me if I liked(like) watching movies.

I agree with Raymott's advice (post #2), but you are right. The present tense is possible here.