At least in the USA, the -re suffix (as used in the Queen's English) is typically replaced with -er...when a typical American English speaker sees -re, it is most likely because the word is not English and intended to be pronounced as "ray", since they are aware that the ending is pronounced that way in foreign languages. Libre certainly is a "foreign word" to us. American English speakers do not look at -re and think that it sounds like "er", unless they know they are reading text that is intentionally written/spelled in the Queen's English. To use your litre example, we would not write it as "litre", it is "liter". However we are certainly aware that it is a non-USA spelling of the word and that it should be pronounced the same as if it were liter.
I don't think typical American English speakers have a problem actually pronouncing the -re ending as "ray", however it is a longer sound, we tend not to have to pronounce it as a suffix that often and it drags the timing of the word out. When we say "LibreOffice" it drags the tempo and rhythm of the speech down in the middle of the name in a very odd way with that combination of vowel sounds. In our normal speech there would be a stop or consonant/plosive sound between those vowel sounds but in this case is intended to be pronounced as one word. Because of that, it feels uncomfortable to pronounce. It's not so much the "Libre" in and of itself...it's the combination of Libre and Office together.