Romanticising can show up with kore than just heavy topics, and it's important to distinguish between romanticising (which is often about a situation) and character/narrator perspective (which is more about tone). It's possible for perspective/tone to romanticise something - but it's usually acceptable if done with meaning and purpose and/or if it's accurate to an individual and how they think. However, it should still very much be kept in check and here are someway it tends to pop up:
Wrong tone - the narrators tone doesn't fit the event, usually propping it up in a 'good' light when it's clearly a wrong act. In general, an improper tone isn't right to use - however it can also show narrator perspective really well. A murderer isn't going to narrate someone getting shot the same way as a volunteer at an animal shelter would; someone who doesn't see an act as 'wrong' or 'a big deal' won't narrate it as such. Not all narrators are 'ideal people' (they really shouldn't be to be interesting) and their perspective should affect the tone of the description. So, look at you narrator and decide what hind of tone realistically fits for those heavy topics given who they are.
Ignorant character/narrator - this is related to tone in that a character will narrate based on what they think of life and situations - which can come from romanticised ideas from a community, culture, friends etc. Romance is often romanticised (until the person enters a romantic situation and then the view is corrected), as is violence (especially the idea that it solves problems easily, when it really doesn't). Not everyone has a clear view of reality and that can be reflected in writing. Some writers choose to have a more down-to-earth character to help correct this narrator or at the very least how the reader that the narrator doesn't have an accurate way of thinking.
No consequences, or unrealistic ones - this is the real issue behind romanticising. Characters get away with things they shouldn't have, reality doesn't kick in when it makes no sense not to, r situations are just unrealistic in general. There are some characters who actively try to avoid the consequences or just live in a way that lets them, and that's okay as long as it's made lear that it's not normal nor an 'easy escape.' You can have a character who thinks romantically about something, but then learns the reality later on because of consequences.
It's important to realise that consequences can appear in multiple ways; social, economic, physical, emotional - realistic consequences touch on all those elements (one more, I'm sure I forgot some). It's easy for writers to focus on punishing a character for bad acts with events that humiliate or cause pain, but it's often better to focus more on how the characters life would be affected more subtle ways (or not so subtle, depending on the reality behind the issue).
It's often very powerful for a character with a set idea of something (a romanticised ides) to experience reality and change that thought - often more so than just having a character who knows what's right 24/7.
General stories aren't moral tales (unless you're purposefully writing one, but I don't think you are), and even if they were, sometimes bad people get away with and things. While romanticising is definitely bad, a degree of it can be true to certain aspects of life and it's okay if you want your writing to reflect that in how your characters think. Romanticised situations and consequences are where the real trouble begins. It's not the writers job to beat readers over the head with an idea that something is bad (if you want to, then write a moral tale instead of a story for entertainment) but realistic consequences are often the best way to avoid romanticising while keeping an interesting story.
You can still have a character who avoids romanticised tone, ignorant, and suffers realistic consequences, but you want to be careful not to make them too 'perfect', particularly with thought and perspective. Everyone has something that they romanticise in one way or another, but it doesn't necessarily have to be that heavy subject you're writing about. It really depends on the story and subject as to what level of realistic romanticised perspective that you're willing to work with.
Realistic consequences are the key! Perspective and knowledge can also play a part in avoiding romanticised things, but you want to be careful to make sure it's accurate and the narrator still has the appropriate tone and the knowledge for who they are.