I am not sure about this as I am not the author of this solution but notice the existence of singular "they" https://en.wikipedia.org/wiki/Singular_they
I personally don't like it too much, but I am not English and I am male. I see it reasonably often being used in situations where gender neutrality is very important. Especially in academia it appears to be becoming more and more popular.
Notice that the proponents of singular they usually dismiss fears of possible confusion, like yours, as a minor problem.
“They” used as singular here doesn’t work, as it's only used when you don’t know the sex of the speaker or it's a “he or she” situation, which seems extremely unlikely if you know that the speaker talks only about their husband (therefore making clear that you know who the speaker is). As you can see, in the latter sentence “their” works, only because “the speaker” can be either male or female in this non-specific example. However, the minute I refer to an actual person I know, “they” cannot be used as the subject, and it would be odd to use “their” before husband. This is not the best explanation, but it would take too long to explain more fully.
I am sorry; I admit I felt you were being sarcastic with me, hence my reply. I see that you did not quite grasp what I was trying to say, and, as I thought, my reply was not entirely clear. I'm not commenting on the acceptability or existence of gender-neutral or gender-fluid people. I still find the sentence odd, but there is no further purpose in arguing about it.
But the question is not whether it works in English (I'm sceptical about that) but whether it works in Czech. If it meant "They only talk about their husband" how would a Czech interlocutor understand that? Would they (sic) think of singular they? Or of a polygamous relationship? Or just raise their eyebrow(s)? If mluví doesn't work as a plural verb in Czech by context, then it shouldn't be accepted as a plural verb in English.
I don't understand. How can you ask whether something English works in Czech? They .... here is an English sentence and it is a possible translation of the Czech question at the top.
The Czech sentence above can indeed mean that multiple persons speak about their one common husband, yes it really is one of the possible meanings. But the most common meaning is the official one "She talks...".