The USA nominally practices separation of church and state, and does not normally recognize individual religious laws - whether that be canon law and courts, Jewish law and rabbinical courts, etc. - and I know this has sometimes caused difficulties in the case of Quaker marriages, because the form doesn't follow the (Christian-influenced) procedure. Has this ever caused issues with the recognition of Jewish marriages in the US?
Since marriage has generally been governed by state law, you'd have to look at each state to find an example. On the other side, for example, but Rhode Island has long recognized Jewish Marriages that would otherwise be barred by the state's consanguinity laws (i.e, laws proscribing marriage between close blood relatives).
"§ 15-1-4 Marriages of kindred allowed by Jewish religion. – The provisions of §§ 15-1-1 – 15-1-3 shall not extend to, or in any way affect, any marriage which shall be solemnized among the Jewish people, within the degrees of affinity or consanguinity allowed by their religion. " https://law.justia.com/codes/rhode-island/2012/title-15/chapter-15-1/chapter-15-1-4/
According to this article, the law has been in place since 1764. https://www.jstor.org/stable/43057881?seq=3#metadata_info_tab_contents