About the only way neck-turning weakens the case is if you get stupid about it. Get a cutter w/ a bevel on it that matches the shoulder angle so you don't gouge the shoulder region when turning the necks.
BR shooters turn the necks of some calibers down to as little as ~9 thou - coming from ~13 thou or so. Thats one hell of a lot compared to what I've seen most people do, and can be an invitation for donuts in the shoulder/neck region. Most folks, even with 'target', but non-BR rifles don't have fitted chambers where you have to turn the necks to fit the chamber. They may be snugger than SAAMI spec, but usually not that tight.
Turning for a light clean up as mentioned, or to a specifc neck diameter for consistency, is one of those things that can't hurt. More consistent neck thickness generally equals more consistent neck tension, and more consistent bullet release. It is a matter of increasingly small benefit, though, and you probably need a gun/load/trigger puller that are working really well in the first place to be able to really tell the difference in sheer accuracy. The other place it may show some benefit is in more consistent muzzle velocities. Again, the gains are small, but generally real - if you sample a large enough population of cases. Shooting 5-10 of turned and 5-10 of un-turned might give you different results than say, 50-100 of each. It also depends on how consistent your original brass is to begin with. Traditionally, Lapua match brass is very consistent, and a lot of folks load it and shoot it and have excellent results. The batch I got this year (900 cases straight from the importer) were... not so good. Then again, my standards are a bit higher than some. Neck turning to clean up inconsistent cases is one way of *making* the necks consistent. Others say (and I can't entirely disagree) that those thick/thin spots don't stop at the bottom of the neck - they likely go some distance down the case shoulder and body, and may affect how the case as a whole expands during firing (getting really nit-picky here). Some folks sort cases by runout (measuring that thick/thin ratio) first, *then* neck turn.
Me, I neck turn pretty much all my match cases because as mentioned, done right it can't hurt and it *should* help.