Semantics around the world "bullying" aren't really important to the bigger issue. No matter who is in office, a grand shitload of misogynistic things get said about the first lady. It is completely unproductive and ridiculous.
Gonna beat a dead horse (and this will be tl;dr anyway), but you would be pretty hard pressed to find many misogynistic things said about this first lady on VVO/SLU, let alone a shitload of misogynistic things. In addition, you generally won't find a lot of liberal-backed misogynistic things said about this first lady. Of course on the internet you can find pretty much anything if you try hard enough, so I am not going to say there is nothing misogynistic ever said about Melania by liberals. However, misogynistic rants are, by and large, a conservative MO.
You also said things like she is ONLY a gold digger and that it is not immoral to be a gold digger if both parties agree on her being a gold digger. I don't agree that she is only a gold digger, she has shown herself to be callous, shallow, and cruel (though that does fit in with the gold digger stereotype). As to the immoral aspect, sure, the agreement itself between both parties is not immoral, but there is a shit ton of immorality going on by her being a gold digger to someone who she knows is a narcissistic criminal. It is akin to knowingly using sweatshop labor to product merchandise or gaining profit from blood diamonds (that white colonist outfit she wore to Africa does fit the role of blood money heiress). When it comes to gold digging at the billionaire level, it is fair to expect that a big chunk of that money is obtained (at the very least) immorally, if not outright criminally. So it is a bold faced lie to say the billionaire gold digger is innocent when she knows where the money comes from. She accepted blood money, therefore her hands are stained.
The fact that she is a gold digger to Trump is grounds for criticism, which kills your whole aversion to the guilt by association issues. But on top of that, even if you remove the whole Trump association context, her actions are despicable. FFS, she literally wore a coat that said "I really don't care. Do U?" when going to visit detained children.
Do you think it is a coincidence that her "cause" is anti-bullying? What is her vile husband constantly blabbering about? Does: "This is the biggest witch hunt in history" ring any bells? And now she is claiming the same over-bloated bullshit as her asshole husband; that she is the most bullied person on the planet. Melenia and her "cause" is not an annoyance, as you put it. It is another facet of Trump's fascism and it is part of the bigger issue.