Just to play devil's advocate (not that I'm discouraging filtering) and just so there is a balanced view of the situation, the downside risk is introducing contaminants during the filtering process itself. If the lipophilized vial and the contents are sterile, then the best thing would be to reconstitute directly into the source vial. For filtering to be most effective, all the supplies used need to be sterile and an aspetic as possible technique needs to be followed. That's a lot of unknowns.
A good example is tesamorelin which is prescribed in lipophilized vials and patients reconstitute. They don't reconstitute and then filter. The reason is that the product is pharma grade and sterile. Since we don't know the actual sterility of our vials, the default is to filter. But I totally understand why some people don't filter and I don't judge them. We have a substantial "grip it and rip it" cohort here and no need to make them feel like they are doing something wrong not spending a few bucks.
The reality is that as a community we do so little sterility testing that we really don't know what we're dealing with. And even when we test it's a vial or two. Nowhere near enough vials to draw any conclusions. I filter every vial, but understand why some people don't.