No conflict of interest really, a free market allows the owners and the employers to work out a mutually beneficial market solution. For employees, that might be a better benefit to be in a union.
Employers may go into a market as a 'union' as well, just like all the airline partnerships.
It is only a problem when govt favors one party over another. Nothing perfect, but squares with the market. Naturally both parties desire the politicians to favor their position.
Unions are not the answer for all employment situations, but it isn't actually a liberal/conservative scenario unless one limits their thinking and are strictlky partisans. YMMV