I had to postpone my reception date to Next April because of Covid, but still having a small ceremony on my wedding date this October with about 10 family members. Should I still leave my registry up on my website?
I think so. People might still choose to send you a gift on your original date or at the very least it will be there for your April reception. I'm getting married in March and our registry has been up for a while. Just check on it periodically to make sure items aren't discontinued or changed
You don't need to take it down unless your website says, "we're still getting married, but you're no longer invited to ANY of our wedding-related events." Ours is still up. I changed the date on our wedding website to our new reception date and I decided that I'll change the date on our registry to that date when it gets to ne within a year (I don't have a good reason for waiting to go this).
Some people will want to buy you a gift no matter what happens with your wedding. You may as well guide them to things you like!
Definitely leave it up, but check periodically to update it with new items as things sell out/become unavailable. When I postponed, half my registry became sold out, so I had to redo a lot of it.