Synthetic oil has a more consistent molecular structure and purity than "regular" oil. It won't make a clutch slip any more than "regular" oil.
That said, you don't get offered to buy pure synthetic or "regular" oil, as it is sold in a formulation blended with additives. The wrong additives can make your wet clutch slip and your seals swell, or leak, regardless of the base stock used. There is also the issue of prior oil selection/usage leaving sludge, that can be loosened in chunks when converting to a high detergent oil.
You can't even rely on a brand name because they are under no obligation to keep the same formulation from batch to batch. Brand names of 5-10 years ago, is almost certainly comprised of a different formulation or additive package today. And, last year's September batch can be different than last year's October batch, if the company determined a formulation change was beneficial to them. What the consumer doesn't know, won't make a sales quantity difference to them.
Without an extensive and costly testing program/effort to determine failure/non-failure patterns, you can only hedge your bets by using what the label says is formulated for wet clutches or what Honda states/recommends for the engine they manufactured.
The forum's personal "brand/type loyalty", anecdotal recommendations as a subset of the general public, are as reliable as a weather forcaster's predictions for next thanksgiving holiday weekend.