Toxic masculinity is part of it. Men used too and still are taught to be manly and not show their emotions, when thats actually very harmful towards their development.
In recent years this has gotten better and not every household is like that but it is still a thing especially in places that are more conservative.
As someone previously stated, generally the people who hate feminine men also are sexist against women.
Not only that, I believe part of the shipping issue is from a female standpoint is attraction. Straight women tend to be attracted to spectrum of masculity, leaning to less feminine men. I assume thats the primary audience of Hetalia. Obviously everyone is a individual and I am not implying there is anything wrong with being attracted too or being a feminine male, but as a woman thats just my perspective on the shipping/fandom part of your post OP. I should also state that no man or rather healthy one is 100% masculine or what we perceive as such.
PS: I am not implying that if you are feminine women won’t like you, I hope this part of my post doesn’t come off that way.
I would say it also could be homophobic, as thinking a feminine character needs to be with manly one seems to push the straight ‘dynamic’ more than the characters actually having chemistry. I think generally hating feminine men also could stem from homophobia as well, because unfortunately that is a stereotype that is very common.
In the end I think its a large amount of issues wrapped into one and I think the Brony fandom is honestly helping to tackle this issue, because many bronies are being proud to like a show thats considered feminine.
Regardless, always be yourself and don’t listen to the haters