Well, since you're using postcrossing and I have done so myself as well, take a look at their community guidelines:
All postcards must be registered.
These include those that might not match your personal preferences or taste - all postcards must be registered, no exceptions. If you receive a postcard without or with a wrong Postcard ID, Postcrossing can help you. If you've received an item that you feel is unsuitable for the project, you should report it to Postcrossing and we'll look into it.
Use your profile to write about yourself.
Your account's profile is the place where others can learn more about you, so please enter a few sentences. If you mention which postcards you like in your profile, keep in mind that others are not obliged to send you a postcard that matches your preferences. You can not make demands about what you want or don't want to receive.
So basically, when using this you can't force people to not send you postcards you don't like. But I think you could report some of the things on your 'dislike' list (specifically the ad cards or nudity, maybe LGBT themed cards as well since I can imagine receiving one in the mail can bring you big trouble in some countries), under the first paragraph, as "having received an item that you feel is unsuitable for the project".
That said, it might help to include some reasons as to why users should not send you certain postcards. I've seen you around for a while, and I think that you could explain your preference for not receiving most of the cards you listed as a consequence of your religious beliefs. So, if you want to go ahead with attending other users to the fact that you did not like their postcard, I recommend adding this information to your profile.
Explain why you wish to/should not receive such cards. If true, you might in some cases even state that having cards with certain themes in your possession could bring you into serious trouble.
Adding this to your profile should help people understand the reasoning behind you finding pigs appalling animals for example. That being said, you can't expect people from entirely different cultures to understand your religion completely, so you might always get postcards that aren't completely suited. And there are always the not very nice people on the internet that will send you a postcard just because it offends you. Register the cards as having received them, burn them and move on to the next, hopefully, better exchange.
Since you stated that you really want to address this in a registration message, which I do not recommend:
- Start the message with a 'Thank you' anyways. This will make the message read a lot more polite --> You should always appreciate the effort that people took of sending you a postcard, even though the card itself was not to your liking.
- I'd make it very clear that I liked the gesture, if not the postcard itself, before even moving on to criticizing the postcard.
- If you criticize the postcard, make sure it is 'constructive criticism'. Use a 'patient' tone of voice. Maybe explain that because the card conflicts with your religion, you can't keep it as a nice memory, and that you are sad that you had to let it go. And then gently attend the sender to the fact that these restrictions were already on your profile, and ask them to see this as a kind reminder to carefully read the profile of the next person they are sending a card too, since you wouldn't like to see those people disappointed as well.
- End with another 'thank you for the gesture' or maybe for their kind words that were on the card. Make sure your message ends on a positive note: always sandwich criticism between two good things.