Is it safe to cut off some parts of the faceplate?

haha... that`s totally sounds like me 😀

Yeah, faceplate is just the braket use to secure your card and hold any output ports so as long as you only trim faceplate it self it`s fine.
However I strongly recommend you remove faceplate of the card before trimming anything no matter what tool you are using.
That`s to avoid any grain of cut off metal to go on your card pcb.
Also before you fit faceplate back make sure you clean it properly for the same reason mention above.
Hope that make sense
 
Cutting off pieces of the plastic shroud depending on location might be possible without affecting performance, pictures of the area you are looking it cutting off would be useful in helping you determine if it is safe or not.
 
In theory, you should be OK.
But these parts are very standard. If something does not fit, then you should find out exactly why.
Often one is trying to insert the tabs where they should not go or some other such reason.
I would be more inclined to trim the case than the card itself.