IG? Yes, they've got two arms, two legs, two eyes and can die for the emperor. They're qualified. Odds are they're going to die as a guardsman, but there's always the chance they rank up.
Commissars? Unlikely, their recruiting pool is exclusively orphans of war. A local commissariat may recruit Felinids, but like all local commissars, they are 2nd class to the Imperial brand.
SOB? Hard no. An anomaly is possible, but strictly speaking, even a Felinid taken in with the Ecclesiarchy would be unlikely to be called to the order militant.
Preachers? Possible.
Arbitrators? Completely feasible, but they would likely find themselves unpromotable. Local arbitrator orders would be more likely to permit the abhuman.
Scribes? Are you literate? Can you write quickly and accurately? How do you feel about twelve hour shifts? Welcome aboard, here's your pen, your parchment and your blister guard.
There is no qualification of being a High Lord that would make a Felnid impossible to be one, beyond the obvious political disability of "Is an abhuman", which makes it unlikely for them to rise anywhere near that level.
Abhumans are accepted for the utilities they provide. Ogryn are appreciated as shock troopers. Ratlings are useful as snipers. Felnids are decent scouts.
In setting, they have the same mark of distain as any other abhuman; They are only more acceptable because their mutation is not always aesthetically disturbing, and this is more an issue of social cloaking rather than actual greater acceptance.
Catgirls are treated like shit in the Imperium by proper imperial citizens user. They only escape the same way anyone in the Imperium rises above their station: Exceptionalism.
The only abhumans that get away with it are Navigators, and only because they're irreplaceable to the point of being given their own category simply to pretend they're not highly deviant genomes.