It's interesting how varied the tastes are in our little hobby among its enthusiasts. For me, I cut my teeth on aromatics and virginias, and those are two styles I still enjoy, especially the latter. But burley-forward blends (as opposed to blends where burley is just a common component) have been far and away my favorite. I love the nuttiness, breadiness, and light touches of cocoa; I love how readily burley takes to light and offers a thick smoke; I love how burley, when properly proportioned and used, can balance out overly sweet virginias and provide needed body and oomph to an otherwise airy aromatic.
But I totally get why others do not take to burley as I do. I never was a cigarette smoker, so I never been one to jones for nicotine badly, but even so, I am not sensitive to it whereas others are. Some don't find the natural earthiness of burleys to shine through and instead taste a more ashen flavor. Even I will admit a lot of burley blends tend to peter out in a bad way at the final third or fourth of the bowl (with some exceptions of course). A lot of people love Latakia, and I think it is overrated and overpowering. I still enjoy a Latakia blend now and then, but it is not normally my first choice.
That all being said, in keeping the spirit of the OP's original inquiry, here are some blends I would recommend to burley haters and why:
C&D Briar Fox: Plentiful virginias help balance the blend, and it has a natural spiciness that is enjoyable. It's the chocolate chip cookie of VaBur blends, but it is a chocolate chip cookie made at home with love. Not saying a burley hater would like this necessarily, but they would enjoy the virginias at least.
Peterson University Flake: great quality flake with a plum topping that is neither overpowering or underwhelming. For those who hate burleys because they taste too plain, this is worth a try.
Savinelli Jupiter: It's not everyone's favorite, but I like it. A burley bomb with some DFK and rum in the background. There's a lot going on, which may entice a burley hater.
Velvet: It's a codger blend, I grant that, but it is one of the smoothest codger blends with a touch of liquer sweetness. May be worth a try, especially for those who find burley too strong or rough-edged. Plus, you can get a pouch for like $5. It's cheap as dirt.
GL Pease Barbary Coast: A love it or hate it blend, but I love it. Topped with brandy and heavy on perique, it has a very fruity, plummy character that is held in check by the wise use of burleys that help keep everything grounded.