RNA is sensitive to RNase present in the working environment, skin, and others. Although it depends upon handling, use of RNase contamination removal sprays and others, but use of filtered tips would be advantageous providing protection from aerosols from pipettes and environment.
depending on the RNA harvest / isolation protocol you are using, the lysis buffer may already contain RNA stabilising agents or Rnase-inhibitors, since your cell or tissue material as well as the tubes you probably use during cell harvest may very well contain Rnases anyway - so technically, it does not make all that much sense to add the lysis buffer with super clean tips. However, (in my opinion), being extra cautious with regard to "cleanliness" when handling samples destined for RNA isolation is never too much of an effort.
You can clean your working space and pipets etc with commercially available agents and/or with 0.1M NaOH, 1mM EDTA.
I completely agree with Katharina, things like eppendorf tubes etc may already have some RNases on and being extra careful isn't any effort.
Saying this I worked in an RNA lab for 3 and a half years, and I didn't use a filtered tip once because its all about technique! The biggest enemy to your RNA samples is you and RNases on your skin.
So when you do your RNA isolation, I would recommend using sterilized normal tips and eppendorf tubes. And then whilst doing your RNA extraction, during your incubation periods, just relax and don't let your gloves touch anything unnecessary, especially your phone which will have tonnes of RNases from your skin and face!
No need to use filter tips. If you work with small amounts of RNA, use RNase free-certified material. It is not the same as filtered or autoclaved. They are sold by many suppliers (cheaper than original Eppendorf). If you have large amounts of starting material, it does not matter.