why does it need to be RGB in order to use some filters?

Regarding the CMYK to RGB to CMYK question, a lot more info needs to be posted, there are too many unknowns. Colour may or may not change noticeably on screen, however, the colour values could be rebuilt in a way that results in different output.

If you really needed to preserve the original separation values, there are tricks that could be performed to do so – as long as the steps can be captured in an action or manually performed exactly the same on two different files. 

And if I do convert it back to CMYK after I did the filter, will the colour change?

By @maryw24984106

Yes! 

The very last step in your workflow should be converting to CMYK! For many reasons (we can go into if you wish). 

I would like to know why that is.

The simple answer is math and how color spaces in the computer are defined plus simplicity. You wouldn't make your life complicated by worrying about color conversions if you don't need to. Of course it could be argued that PS should handle a lot of this without even bothering the user, but that's just how it is.

Mylenium

Some Photoshop Filters are old and have other limitations to boot – no meaningful preview, don’t work for 16bit, …. 

But I suppose in many cases making them work for CMYK would just be a waste of resources as CMYK is for final print output, not for editing photographic images. 

Any color conversions has an effect and quantification can add up, so it’s best to keep the conversions to a minimum. 

Ideally work on profiled RGB-images and convert to CMYK once – namely at the very end at pdf-creation for the actual specific printing-process. 

In some very specific cases (definitely known CMYK Space beforehand, fine pure one-color linework or type, …) it can make sense to work in CMYK, but generally when it comes to photographic images it does not so much.