The other thing to consider with bitterness is that bitterness presents differently depending on the other components of the beer, such as the SG:IBU ratio (or IMO the more accurate FG:IBU ratio) - the sweetness of the beer will counteract the bitterness, leading to the beer tasting less bitter or more bitter, even when at the same IBU.

OP, If it is the not the hops bitterness that is specifically unpalatable for you, but the hops flavours, you might be interested in Gruit, as it replaces the hops with herbs for the bittering component, replacing grass, pine and/or resinous bitter notes with spice at the end of the palate, or a Graf, which combines beer with cider, where the Malic Acid in the apples helps to balance the sweetness of the beer, reducing the amount of hops bitterness needed. You could even combine these two styles, making a spiced apple juice beer that does not use any hops to balance the grain sweetness at all.