What's a decent way of responding? What should I keep in mind? What mindset should I have?
You could keep in mind the Fundamental Attribution Error, which observes that humans tend to see our own mistakes and problems with the viewpoint "I'm fundamentally a good person, but on this occasion I did something wrong", but see other people's mistakes and problems from the view "they are fundamentally a bad person, they always to things wrong".
The complainer is probably not fundamentally evil, nasty and hateful. They are probably a normal human who likes and cares about very similar things that you like. They are a programmer, they found your app, they are interested in whatever your app does, they used it enough to find the bug, they cared enough to report the bug report instead of giving up; but they were angry and lashed out at you.
You are overlap a lot with this person, you have more in common than if they were a 50 year old conspiracy theorist who doesn't know what Android is or what your App does, and sent you a rude email about how you are doing everything wrong by using evil computers.
You wouldn't be bothered by that person at all, would you? It wouldn't strike a nerve, you might even laugh at it.
I care a lot about our users and want to maintain a good relationship and a good rating of our app. On the other I'd feel like a complete sell out if I would reply overly polite.
If you care more about App ratings than about keeping yourself feel good, you are a kind of sell out. If you care more about your users getting a good experience than yourself feeling righteous, you are a kind of sell out.
This is good, not bad. In the context of making your app the best possible app, it's not about you the author, at all. A cathedral builder will have to overcome a lot more problems than hearing some rude words to build a cathedral. A cathedral will stand for hundreds of years and countless people will wonder at it, what does a rude word to the builder in the first moments of it's construction count for? 0.00% of anything. The builders have better things to do than spend effort fighting back, more important things than putdowns.
Is the point to make something as good as you can, or be self-righteous, bitter and nitpicky over small details and individual user accounts?
Is the bug genuine, and can you fix it?
Do you want a world where people respond to anger with anger, or a world where people respond to anger with kindness?
Ideally you would only get polite bug reports. That's not the real world. So would you prefer some rude feedback about bugs, or to not hear about those bugs at all?
If you were rightly or wrongly feeling disappointed and let down by a piece of software and were extremely blunt about it, what kind of reply would you feel good about getting?
Is it really as strong an attack on your App as it feels like? Are you about to lose funding, lose users, fail at your goals completely, have your department shut down, if you don't fight back?
I agree with the "don't take it personally", "be magnanimous" and "fix the bug, ignore the rudeness" people, I just wanted to write more than would fit in a comment about why and how you can frame your thinking to make it completely 'OK' to do that.
-- Edit; actually I want to write more than that --
There's nothing to actually stop you being rude right back. You exist in a post-God world where you don't believe being rude will send you to hell (I assume, otherwise you would have immediately thought about all your religious teachings on how to behave towards others), you are writing a free app so there's no business pressure on you to be unfailingly polite, and you are involved in programming - a pretty relentless technical meritocracy culture with prominent examples of leaders have a rude attitude under the guise of being 'no nonsense', and a culture of flame wars and anger.
In short, there's no higher pressure on you to arm-twist you into a polite reply and you are absolutely free to reply in kind with:
I wrote this for me, if you don't like it, tough.
I wrote this and gave it away for free, how dare think you have any grounds to complain, do you know how much passion I've put into this, I'm so offended right now.
It's open source. Why don't you improve it and submit a patch? Hope this helps. /smug :)
You are an idiot, here's a rant about everything wrong with you and your mother as well.
That was rude so I ignored it, lol. :)
And so on, and there will be no short term immediate consequences whatsoever. Short term, you will feel better. Justified, happy, correct, superior.
So why should you take a personal hit, and feel hurt, feel undervalued, and reply politely in the face of pressure not to?
Because without any higher guiding principle the only thing you can do is step back and ask yourself what kind of a world you want to build. Everything you do is a contribution to the world of the future. Do you want to contribute to a ragey, firey, inhuman, uncaring, technical meritocracy? Or do you want to be a calming, humanising influence, a relatable developer?
I'm leading it towards an obvious conclusion here, but it's not anymore a question of absolute, externally imposed right and wrongness, so maybe you will genuinely land on the other side from where I'm biasing it.
Torvalds swears at incompetent people. Knuth offers money as rewards for correct bug reports. Both are respected and successful.