Why interference still occurs when a beam of red light passes through a hole created by the slits? The screen captures different brightness of red light.

If there are no interferences took place, the brightness should be uniform.

Could you clarify what you mean by "a hole created by the slits?"

--- Hole ------ slit

 

--------------Wave

--------------Wave

 

The situation as if this one represents.

So there's basically two slits of differing sizes? You should still get interference. But with a hole that's very wide you will probably lose contrast. Diffraction effects come into play when you look at the slit/hole sizes. As the hole gets big the diffraction peak gets narrow, and you won't see the higher interference orders.