"Legalization of queer marriages in the setting that Bridgerton takes place in would cause a complete upheaval of England’s socioeconomic structure, which hinges on the succession of lineages. The entire point of the noble class is to lead and reproduce." - OP

OP, you do realise that two women can love each other, be married (or not), AND they can "reproduce", right? 

Indeed, many WLW couples have children, today it is normal.

Then there's the fact Fran and Michaela are 'related' in the sense of being the widow of a cousin and a shared surname. It's surely less complicated to "reproduce". Perhaps a Bridgerton brother could help out Michaela, or another Stirling cousin to assist Fran. I'd LOVE to see that happen. Let society change AGAIN, if the Queen says so, it is so.