the thing is that she’s not adam; she doesn’t have the weird reality-altering powers he did that can bring about the end of the world just by thinking about it. she’s actually no more powerful than any lord of hell or highest order angel (ie: Archangel with a capital A, seraph, cherub, throne) and can’t really do anything that they can’t also do. if anything, her abilities are slightly diluted by only being half divine and half infernal, which means they’re at odds with one another - her body is constantly attacking itself in an attempt to cancel out the conflicting energies -  not to mention she’s vulnerable to both angelic and demonic weaknesses (although she’s slightly less affected by them than a ‘pure’ angel or demon would be, so if you wanted to dunk her in holy water, say, you’d have to keep her in there for several minutes like one of those fizzy vitamin tablets until she disintegrated completely, or she could just regenerate), so if it came to a straight fight any angel or demon in the uppermost tiers of the heavenly and infernal hierarchies could wipe her out without significant effort on their part. 

there are actually 2 ways that heaven and hell finding out about her could start a war. the first hinges on the fact that she’s literally an abomination - half angel/half humans (nephilim) and their descendants were drowned in the flood (the noah’s ark one), so a half angel/half demon child would only be even more horrifying a concept in heaven and hell’s eyes - and so heaven and hell would simply go “okay, time to clean up this mess” and, as crowley suggested might happen at the end of episode 6, join forces to pull a “heaven and hell vs. humanity”. the second way is that they might both try to gain custody of her (ie: kidnap and imprison her) and persuade, or failing that force, her to pledge her allegiance to them so that they have an upper hand on the other side by having possession of her (they don’t know what she’s capable of, after all - as far as they’re aware she could be an even bigger threat than adam), which would trigger a war since the side who didn’t have her would be like “hey, that’s not fair” and attempt to gain possession of her themselves by taking on the side who does.

tl;dr: if they find out, everyone’s fucked, not just her parents (but they’d probably be the first necks on the chopping block).

the thing is that she’s not adam; she doesn’t have the weird reality-altering powers he did that can bring about the end of the world just by thinking about it. she’s actually no more powerful than any lord of hell or highest order angel (ie: Archangel with a capital A, seraph, cherub, throne) and can’t really do anything that they can’t also do. if anything, her abilities are slightly diluted by only being half divine and half infernal, which means they’re at odds with one another - her body is constantly attacking itself in an attempt to cancel out the conflicting energies -  not to mention she’s vulnerable to both angelic and demonic weaknesses (although she’s slightly less affected by them than a ‘pure’ angel or demon would be, so if you wanted to dunk her in holy water, say, you’d have to keep her in there for several minutes like one of those fizzy vitamin tablets until she disintegrated completely, or she could just regenerate), so if it came to a straight fight any angel or demon in the uppermost tiers of the heavenly and infernal hierarchies could wipe her out without significant effort on their part. 

there are actually 2 ways that heaven and hell finding out about her could start a war. the first hinges on the fact that she’s literally an abomination - half angel/half humans (nephilim) and their descendants were drowned in the flood (the noah’s ark one), so a half angel/half demon child would only be even more horrifying a concept in heaven and hell’s eyes - and so heaven and hell would simply go “okay, time to clean up this mess” and, as crowley suggested might happen at the end of episode 6, join forces to pull a “heaven and hell vs. humanity”. the second way is that they might both try to gain custody of her (ie: kidnap and imprison her) and persuade, or failing that force, her to pledge her allegiance to them so that they have an upper hand on the other side by having possession of her (they don’t know what she’s capable of, after all - as far as they’re aware she could be an even bigger threat than adam), which would trigger a war since the side who didn’t have her would be like “hey, that’s not fair” and attempt to gain possession of her themselves by taking on the side who does.

tl;dr: if they find out, everyone’s fucked, not just her parents (but they’d probably be the first necks on the chopping block).