Until 5 minutes ago we knew that the baby change area doesn't trump the sex based nature of the space, just as the sex of a toddler doesn't determine which space parents use - mums don't automatically bring their male toddlers into the men's and there is no equivalent need for (boundary pushing) men to bring their daughters into the ladies.
A changing table is a really helpful add on to the original sex-based facility but, like many others on the thread, my husband and I have whipped the changing mat out of the nappy bag in hundreds of places if one doesn't exist...
Would this example make it clearer for your husband, OP?
I am a woman who has been travelling for hours at an airport. I really need a shower.
I see the sign below.
Some people on the thread (and possibly your spouse?) are effectively suggesting that this space is designed for me because I really need a shower...
And that if the sign was for a women's toilet with additional shower that would be the perfect place for a bloke to freshen up if there happened to be no shower in the nearest men's.
In the real world, as a woman, I would carry on looking for a woman's shower. If I asked and there aren't any for women but just for men I would probably complain about the sexism and ask them to rectify the situation as a matter of urgency. I would then try and do some sort of ablutions in the women’s toilets.
At no point would I think that this sign is for all those who need showers.
I'd be curious to know what your spouse thinks!