But aside from that, and the inherent assumption that beauty standards are universal and biological which is a pretty big assumption.
A slight societal preference does not lead to the conclusions people drew from the article.
To give an example, taller men have a higher chance of being promoted. Fortune 500 CEOs are disproportionately tall compared to the general population. As a society we still promote meritocracy, and working hard. Not telling people who are 5'4 to just give up and be unemployed cause they will never be the CEO of Ford Motor company.
Now you're moving the goalposts, which shows you knew your original claim was wrong. "It didn't happen, and if it did they deserved it" indeed.
No amount of empirical data matters because it is a first principal which the whole rest of the political ideology relies upon. If someone does not accept this as a first principal and is willing to examine empirical data that contradicts it and draw the conclusion that all people are not equal, then they are no longer a liberal.
It’s not acknowledging differences that are the problem. It is things like the assignment of value judgements and other stuff that people erroneously attribute to those differences.
One of the weirdest things about being human is that our preferences are neither rational nor consistent. The classic example in behavioural economics is with ice-cream flavors. If I prefer chocolate to strawberry and strawberry to vanilla, it doesn't follow that I prefer chocolate to vanilla. The preferences aren't transitive, and there doesn't exist a total preferences order.
https://plato.stanford.edu/entries/preferences/#Tra has an overview, note especially the paragraph about pair-wise comparisons.
https://www.econlib.org/library/Enc/BehavioralEconomics.html