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Have you verified that what you 'understand' is in fact the law in Utah?
The above is an information request and not an Answer.
No, I have not.
There is nothing but a semi-informed hodge podge of information on this topic. It's one of those subjects where the "street" hearsay info and all the "understandings" like you have are usually 90% wrong. Everyone you ask has an opinion that is usually based on what they've been told their "understanding" is. You have to find the text of the actual Utah statutes. Here is the closest I could come to Utah statutes. They all seems to involve only violent felons and firearms, but I can't be sure that this is all of them: http://utahshootingsports.com/utahlawsremarks.htm. I can't believe that a 15 year old non-violent felony would prevent you from ever owning archery equipment or a carving knife. But, until you have some local legal eagle gather up all the relevant Utah statutes it's hard to say for sure. You might contact a local NRA chapter and see what info they have. But don't settle for anything less than copies of the actual statutes.
This was inside the URL that I sent you and it appears to have every weapon statute in Utah listed: http://utahshootingsports.com/utahlaws.htm#76-10-503 There are a bunch.