What's the difference between good tropey characters and bad tropey characters? Whether or not you like the tropes present?
I'll just preface this by saying that if we want to enter the world of tropes, there probably even isn't such a thing as non-tropey character or they are extremely rare. All characters represent one trope or another (and can probably be argued to fall under several different tropes). And on the other hand reducing characters to their most dominating trope(s) is often kind of... Well, reductivist and doesn't really do much good for more indepth discussions & analyzes. It's about classification. People love to classify things, even if those classifications can often simplify things a bit too much. It can help in describing things quickly, but usually there's more to everything than that.
That said, in general, I feel a good tropeish character is one that isn't completely one-noted and ruled by the trope that he/she represents. The story either studies the tropey character from different angles & in different situations and/or good tropeish characters can and do develop beyond their trope and even initially have more going to them than their most dominating trope traits would suggest. Complexity & history/context is the key. Humans are complex beings. The class clown usually has more going in his/her life and inside his/her head no matter if he acts like a clown most of the time. The trope needs to make sense.
Bad tropey characters... Well, often it's just a very one-sided character who never really evolves during the story. Some are ones that can represent some deplorable character type while the story treats that as ok or doesn't treat it with the skill & subtlety required or doesn't give context to such characters. Stuff like racist or sexist characters are bad if the story acts as if it's totally fun and super and doesn't really have any connection to the themes & overall story.
That's not to say all racist characters are bad, but racist characters need to be portrayed with some realism, depth and/or insight and make sense in the context of the world/story. Otherwise those characters are there to say racist stuff just because and don't bring anything worthwhile to the narrative/message of the story/whatever. Why is that character a racist, what does that racist say about the world of the story, how does the society in the story respond to racism, what kind of issues might racism cause to the protagonists of the story and how do they overcome it or respond to it etc. The answers to those kinds question are what makes it interesting.
It's really not about liking or not liking characters. People can like a bad racist tropey character but that doesn't make that character a good tropey character. For example, a certain pervy grandpa from Trails of Cold Steel. Some people might find his sexist antics funny, but sexism is objectively bad and so them liking that does not affect the fact that it's a bad character trope.
I'd personally say Angelica falls under a similar-ish bad character type. If someone acted like she does towards my soon to be 14 year old godson, I'd seriously have to fight the urge to kick their ass (and I'm a pacifist). No one in their right mind would say those kinds of things to a 13-14 year old IRL and in no scenario would everyone just laugh it off. Yet Trails of Cold Steel treats that as if it was a hoot. Haha! Look at this borderline paedophile say she'd fuck a 14 year old! How cool is that!?
Of course actual comedy can have a bit of leeway with playing around with some outrageously racist & sexist tropes IF there is something meaningful behind it (usually pointing out the absurdity, hypocricy and/or silly contradictions of some racists or sexist ideologies).