Would a native speaker be able to discern the difference between the pronunciations of "quoi" and "crois" out of context? I am having trouble making the "r" in "crois" noticeable and am wondering if it is not a big deal.
Having difficulty pronouncing the letter R is rather common. The [ʁ] and [ɹ] sounds can be pronounced differently not only in different countries but inside a country as well (as for example in the UK, or in France). More over it is difficult to differentiate the [ʁ] and [ɹ] sounds from the [l] sound. When learning to speak, French native babies will have difficulty pronouncing those two sounds and will say « louge » instead of « rouge » long after they can pronounce other sounds quite well. Some languages don't differentiate at all between those two sounds (some Asian languages for example).
But the fact is that in French differentiating is necessary to make oneself understood in some circumstances. Out of context if you pronounce « crois » and « quoi » in the same way (/kwa/) obviously people won't understand.
But it is very rare to say those words out of context and in context they're very different words that don't belong to the same parts of speech, so it is easy for the listener to compensate and understand what is meant. Same with « trois » and « toit » or « cru » and « cul », etc...
When the words belong to the same part of speech, people might have difficulty understanding in some contexts. For example if you say [ʒə.bwa.dy.pwav] there won't probably be any problem understanding [pwav] as poivre. But it could be understood either as:
Je brois du poivre.
Je bois du poivre.
It can be worse when the situation does not help :
Nous allons le faire à trois
Nous allons le faire à toi.
Although this last sentence is not good French it is a mistake a non native can easily make and that a French speaking person would understand.
I find them all pretty good and constructive, but aimed at English natives learning French.
A native speaker would understand you if you said "Je quoi que j'ai du mal à prononcer les R.", but he would make a quizzical face while listening to you, to say the least