Typically, when you do anything to disrupt the beer, such as pulling trub, you will cause some of the dissolved CO2 to escape. While the beer is still actively fermenting during the primary and secondary stages it is metabolizing in an anaerobic state (no air) because when the air is present the yeast will quickly absorb it to build a cell wall and ultimately bud new cells. The point is if your yeast is active (which it should be) any minor amount of O2, which might enter the beer, would be quickly absorbed by the yeast.
Where O2 really becomes a problem in brewing is during transfers to secondary fermenters, kegs, or bottles that have not been purged with CO2.
In these instances, there may be too much O2 for the yeast to deal with (because of the lack of sugar at this stage). If the yeast is overwhelmed the beer can become oxidized leading and to that wet cardboard taste in your finished beer.
The bottom line: be cautious and try to minimize O2 exposure.
If you are filling a large vessel, purge it with CO2 first. But don't sweat things like dumping trub or dry hopping. These are relatively low-risk events relative to oxygen contamination in your beer and are a part of the process from homebrew to commercial brewing.