Curse tablets were very specific, with specific target name(s) inscribed. It would make no sense for them to be mass produced. Without an actual source or location for the notion that they were "mass produced" it will be difficult to comment, however.

The typical curse tablet (Latin dēfixiō, plural dēfixiōnēs) in the Roman period was a small sheet of flattened lead, upon which was inscribed the curse itself. The lead sheet was then deposited at the target's location (in a crevice of a wall, under a floor, buried in the sand of the arena or circus, etc), usually rolled up like a lead cigar. It is very possible that "blanks" of the lead sheets themselves could have been mass produced, sort of like buying a nice sheet of stationary today. Perhaps that is what is being referenced. We think that curses were an industry, and that one would employ a professional curse-writer to compose the message for a fee. Lead sheets were also used for non-curse correspondence, usually called "lead letters." There is a small but growing corpus of such lead-based correspondence. The reason to use lead for your letter is that it was pretty cheap compared to papyrus, and also durable. I have done some work on "lead letters" and can dig that up if anyone is interested, but that is a separate topic.

It might be that your meme-maker is confusing the ostraka from Classical Athens. The votes for the target of ostracism were written on pieces of broken pottery, and we have good evidence that those were often mass-produced and then handed out in an attempt to influence the outcome of the ostracism.

It's also possible that recent scholarship has shown that the contents/layout of some local subset of curse tablets are identical, suggesting they were all made in a workshop and then specific names were added in. This would qualify as "mass produced." I haven't seen that particular conclusion, though, if that's the case. Study of dēfixiōnēs is a burgeoning field. There are thousands of them found in excavations to date, but in the past they were often ignored and stashed in the corners of dig storerooms because they are difficult to deal with and conserve. It is hard to unroll them without damaging them, they are difficult to read, and their contents are not always particularly exciting for investigators. There are thousands of them sitting in storage. Much like papyri, the list of people who care about their contents and are also able to access them, conserve them, and read them is extremely small.