The "shredded" implies he thinks it's a security issue - that someone else might go through the trash, and a receipt will either let them steal credit card numbers/identity info or find out other things about their lives. (More likely the identity theft thing; 'they're tracking our movements via our garbage' verges on clinical paranoia unless he has an actual reason to think the FBI is on his tail.)

Which - "Do receipts need to be shredded?" is one of those things that could be an honest difference of opinion between two people. It's mostly safe, but most of us are careful about less risky things every day. ("How much stuff is salvageable" can also be an honest difference of opinion. Some people re-use the takeout trays, some don't. Etc.) (And if he's used to double-checking all his own trash for receipts or things tossed mistakenly, he might automatically do it to hers too as an "I am helping with trash" thing because you always double-check that, right, rather than an "I do not trust you" thing.)

But I feel like "come to an accord on what is trash" is one of those things that you ought to have figured out how to communicate about before a wedding, really.