Non-native-speaker take: I don't care, it just reads a bit "weird" as I learned English before and "theirs" was plural... but I am adaptable.
As long as the meaning of the quote isn't changed I couldn't care less and it seems very important to some people.
What I personally dislike though is the whole "Ask me my pronouns" thing... like "No, I don't care about your gender or sex, as long as I am not interested in a romantic relationship with you - just tell me how to call you and I'll do it, but more effort? No!"
To elaborate a bit more: I find the topic exhausting not because I hate freedom of choosing your own gender or anything like that, but because I personally do not care about your gender at all.
I don't care about your religion, your skin color, your culture, your sex, your gender... I care about individual people but I don't reduce them to a certain aspect of their existence.
Now I find the whole "Ask me my pronouns" exhausting and also rude because it puts pressure on me to ask you about a topic I am not interested in. Like: I get it, there is social pressure, I understand that you're not happy with certain social "norms" and developments. I totally get that and I guess we are on the same side for many of them, but I still do not care about your gender until I care about your gender. (And also, I don't live in your country probably, so your local politics may be of interest, but I still don't like being forced to talk about them before I can ask a genuine question on e.g. a technology topic ;))
Just write his/her/theirs... and I will respect your choice. I will not think less of you, nor will I put you on a pedestal for something I do not care about.