When I send official Postcrossing cards out, I usually ask, “If it is not a hassle, can you please send me a return postcard?”
Does that seem rude?
In return when people do send me a postcard I usually thank them for their postcard and ask them for their address as I would love to send them a return postcard from my country.
This is not the point of Postcrossing. In the official part, it always goes one way. A to B, B to C… not B to A.
In the forum you can swap.
I wouldn’t like to receive such a message. It has only happened once or twice.
Since you asked for an opinion, I will answer honestly that I would find this extremely offputting.
However, please join us in the forums for mutual postcard swaps.
i have received cards with such questions a few times. once just with ‘hello i collect this and that and here is my address’ which i thought was quite rude and i just ignored it.
and once someone wrote it like you, like, hey can you write me a card back. so i wrote in the hurray message that they will receive a card back for every one they sent out. just not from me. so. that.
it’s not necessarily rude it’s just not how postcrossing works. if you like to send and receive cards from the same person more than once then i would recommend joining tags or round robins on this forum, like suggested before.
It’s not rude, but you shouldn’t expect people to do it. Postcrossing is designed as a one way sending of cards to protect people’s privacy & safety & that privacy/safety is very important to many, many Postcrossers. It’s deliberately designed NOT to be an exchange of cards system.
So I’d suggest if you want to exchange cards with other people, to set up swaps in the Forum where people who want to exchange cards with others come to for those exchanges.
I don’t find this message weird… For me, Postcrossing is about connecting, so if I receive a message like yours, I’d send you a message back.
In the same way, when I write a postcard with around ten sentences and beautiful stamps related to what the receiver likes, it’s always great to have a Hurray Message which is longer than just “Thanks for your postcard”.
However, I’d not write a message asking directly for a return postcard, as I don’t want to push people. It also depends on why you want to have a return postcard… Is it just to receive more postcards? Or to have the feeling of an exchange?
It’s not rude but disturbing.
People may feel themselves obligated or uncomfortable. We all have right to ignore such requests.
I think it’s quite fine, and offer to do so in my profile 
I often send “Thank you” cards
so I guess it depends on what card you send, stamps you used and what you wrote on the card.
Personally I wouldn’t mind sending a card back but I find it a waste of postcard space. Maybe if it’s in an envelope you can insert an extra piece of paper for that.
Thank you for reaching out to get some feedback on this! As you can see above, many people feel uncomfortable and a few feel comfortable about it. And maybe you sensed it might not be a good thing, so reaching out for feedback was a good step.
Once in a while someone sends me a special card (like a Gotochi card) and if there’s a return address on the card, I will send them a card back - consistent with their preferences - to say thank you. If there’s no return address (most of the time), I will mention in my Hurray message that I would love to send them a card in thanks and if they would like to message me their address, I will be happy to do that.
Remember that the task of sending an unexpected return card is always an extra task for someone to take on - a hassle of some kind, if only the cost for the card and postage, plus the time spent choosing a card, writing the card and posting the card. So it feels a little disingenuous to say “If it is not a hassle” - that’s exactly what it is. Even among Postcrossers who are here in this community because they like writing postcards. Many people have limited budgets or limited time and you are asking them to give you some of those scarce resources.
However I think you could state it a bit differently (as a few people have done to me) and it would not feel intrusive or presumptuous. If you said something like, “I enjoyed reading your profile and invite you to become pen pals with me if you feel a connection too,” then it feels like a compliment and an invitation instead of an unexpected chore. So that might have a better impact on more of the receivers. 
When I first started Postcrossing I often asked (nicely!) for a card in return.
I was so excited and wanted as many cards as possible.
18 years ago there was no forum, you could not send private messages and you could only have 3 (!) cards travelling at the same time.
I soon stopped, as it was pointless mostly and not part of the game.
Nowadays I offer in my profile to send a card of Vienna back, if someone sends me a card of my countless favourites and tells me the code, so I can take that card out (of my favourites, which are my wishlist).
When I get a card, that I suspect to be in my favourites I have a look and if it is the case, I offer to send a card of Wien back, also if the Postcrosser writes the code onto the card, but there is no addy.
I sometimes get asked for a return card, and it is almost always for (according to my taste!) really disappointing cards. Sadly not every card makes me happy. I wish they all did.
So I ignore those requests.
Maybe send the best possible card, according to the profile, and just put your addy on it (just a suggestion). That opens up possibilities!
By the way, if Postcrossers complain about aspects of the official game these days, I just have to laugh. 
Compared to the “olden days” it is becoming more and more golden! 
A substantial number of members write cards / send cards / get a card in return. Done. Requesting a return card on Official Postcrossing is not the place. If you want to exchange cards, there is the Forum for that.
So, I’ve been asked to send a card to someone after they sent me one and I sent a Hurray message registering. I was a little put off by it and I did indeed not send them a card back.
However, people have gotten cards from me and asked in the Hurray message if they can reply. Which I thought was nice and I gave them my address. And I’ve done the same. Sometimes there is a bit of a connection with people I meet and then it turned into a little friendship / postcard penpal situation. That I think is okay- asking if you could reply to their card and send them one. However flat out asking for someone to send you a card back is off putting I won’t lie.
I don’t get offended by that but as someone mentioned, waste of postcard space to me. Maybe I’d do this this way: instead of requesting that on the postcard, send this person a direct message after getting a hurray message - if in their profiles they state that they’re interested in direct swaps. Then you can both exchange additional postcards outside the official one.
Haha you said my words!
That’s your message on the postcard itself? Or at least part of it? I feel like it’s weird, as if you went to a birthday party and said “here’s your gift, could you give me one back?”
If you just have your return address on it and maybe say something like “I’m always open to exchanging more cards!” that is fine (to me).
And if you want to ask for an address in a hurray message to send a return card to someone, that’s fine.
But don’t be surprised if someone is like me and ignores all 3 versions.
In my experience, if you write your card fully written ,either with your unique personal touch, topic that interests the receiver, decoration, new not-very-known information about the card or the place you live etc, the receiver might love it so much and they might want to send you a thank you card :))
I’ve experienced this more than once
I have requested a return card once - I had a real connection to their profile and wanted to become penpals, but eventually it fizzled out. I often think of this person though, and wonder if it could have continued if postage prices, the ‘hassle’ and the additional responsibilities of postcrossing weren’t obstacles.
Once someone sent me a thank you - I though this was nice!
For me, in the UK, for the price of a typical card and a stamp I could buy half a dozen eggs, 4 pints of milk and a loaf of bread. I have a set budget, and at the moment I’m building up my profile of officials so that I can have more travelling during special events or when travelling in countries with cheaper postage.
I would probably sent a return card if I thought there was a genuine connection, but otherwise I would likely ignore this request, or explain that it was out of my budget in the thank you message.