In the 1960's, the Rabbis of Holland established a rule that if a person came to convert, that conversion could only be effected once all of the Rabbis in Holland had agreed to it. This decree grew out of the fact that a majority of conversions involved people doing so for marriage purposes, and thus their motives and their intentions to keep mitzvot once converted were suspect.
A case arose in 1969 of a woman who came to convert with full intentions to keep all of the mitzvot. However, she refused to accept a modest style of dress, stating openly that she preferred to maintain the manner of dress that she was accustomed to. The question as to whether or not to accept her conversion was brought to Rav Moshe Feinstein.
Rav Moshe begins his response by differentiating between a גר who does not know of a particular halacha and one who refuses to accept one. In the former case, the conversion is certainly good, while in the latter case there is what to discuss. Even though the Gemara says that refusal to accept even a דקדוק סופרים (loosely explained as a low-level Rabbinic enactment) cannot convert, Rav Moshe seems to feel that בדיעבד (post facto), such a conversion could be accepted.
Rav Moshe then brings in various cases from the Gemara, most notably the run of potential converts who came to Hillel with various outlandish requests and conditions. While it is possible to state that they should not have been converted, as their requests belie their lack of sincerity, Rav Moshe accepts their conversions on the grounds that Hillel knew that once he accepted them he would be able to continue working with them and teaching them.
That said, Rav Moshe advises against accepting as a convert this woman who refused to accept a lifestyle involving modest dress, particularly in light of the fact that her main motivation for conversion was for marriage, and thus with two strikes against her, Rav Moshe is comfortable rejecting her conversion.
However, Rav Moshe notes that if the conversion were to go through she would be considered Jewish. Furthermore, he speculates that perhaps this woman did not see the need to dress modestly, since she probably looked around and saw purportedly religious women who also dressed immodestly, and thus perhaps she figured that such a requirement was not essential (sadly, such a situation is all-too-real today as well, as fashion in the Modern Orthodox community often mirrors that of the society around us.).