I thought a constitutional amendment was supposed to overrule a judge's decision. Did I miss something?
The 14th Amendment Due Process Clause is interpreted to guarantee the fundamental liberty of intimate associations (Lawrence v. Texas), so the Nebraska's Constitutional provision hindering those intimate associations cannot withstand Federal Constitutional scrutiny, unless it is narrowly tailored to a compelling governmental interest - which, apparently, this law was not.
That, more or less, is the argument under modern Constitutional Law. Doesn't mean I like it or agree with it, but such it is.