Good

I try to remember that people and relationships are more important than positions. In this situation I would communicate support for something that was important to that person’s achievement. That doesn't make me a Christian or hypocrite; the focus is on the person I care about.

My attitude is less accommodating; I'd just say I don't believe in that anymore, and keep repeating that whenever questioned, followed by looking disinterested, and wandering out of the room until they learn not to ask me.

I don't usually send cards to people anyway, because I think they're stupid. When I was little, the only reason I liked getting a card was that sometimes people sent money in them. I didn't care about the card at all.

You pay all that money and postage and they glance at it, and toss it. It's nonsense. In the case of weddings and funerals, I make exceptions.

If I send a present for a birthday or other secular event, though, I first ask them what on Amazon they would like, then ship to them it for free because I'm a Prime member, include the free gift card, and pay extra for gift wrapping.

Do they still hand out those magic wafers at those things?

So, is your issue with sending your great nephew a card or with the fact they do not make cards for the secular 1st Comm cards whatever that even is? If you don't want to send a card because you do not agree with the theology then maybe a card that is neutral and does not mention the Communion something regarding the child growing so quickly or along those lines.
I get the impression this is more about you feeling left out as a result of not believing so maybe you could share a list of important things you would like to have acknowledged with your family but right now your great-nephew is the one that matters. He is a child and if you are at all close to him then by all means send the card because the last thing he needs right now is for people turning his day to shine into a religious tug of war. By not sending him a card you make a statement about the relationship not the ritual (at least to the child anyway). I remember my family refusing to come to, or acknowledge my events because my mom became a Mormon.
In my opinion whether we are believers or not we should make our decisions using that golden rule and do for him what you wish were being done for you. "Do unto others..." and ALWAYS think of our impact on the children involved. (I hope my words help you make the right/best decision for you and your great-nephew because it is that relationship that will be effected.)

Hopefully the poor kid will get over it.

Best wishes with the family situation!

Personally I've no problem with acknowledging other people's festivals and special days. I'll wish Muslims a happy Eid, enjoy fireworks at Diwali and bang out a few carols at Midnight Mass with the best of them. There's plenty of online services will allow you to customise greetings cards.

If you go to the event take a hip flask with. Any old card will do, just say sorry, I got my dates mixed up !

Have you already sent the card? There are lots of "GOOD FOR YOU" cards for children! I use them for all sorts of happy events...one of them should be more than adequate for this event! Good luck! (If you go to the event...it'll be borrrrrrrrinnnnnnnnggggggg.)