Consumer Reports is a nonprofit. They run experiments and whatnot to determine, for example, the optimal toothpaste for children. 

The link says nothing about them having run any experiments in their quest to make toothpaste recommendations and they recommend toothpaste based on arguments that aren't about their own experimental results. Claiming that a process that doesn't test how effective toothpaste is at creating beneficial clinical outcomes like having lower caries as determining "optimal toothpaste", sounds strange to me. 

Their process might be better than just using marketing processes, but it's very far from actually running a clinical trial that looks at which toothpaste is optimal for dental outcomes. They don't even seem to understand enough of the domain to understand that Xylitol is an active ingredient in toothpaste.

They do not get paid by the companies they test the products of.

That claim also seems wrong given that they say "When you shop through retailer links on our site, we may earn affiliate commissions. 

If you want to approach toothpaste rationally, the way you do it build a mental model of the evidence landscape.

Mixed reports on how they have degraded in quality and sometimes misrepresented how thorough their tests are, but still a time saver for finding higher quality options for things you want long service life from like home appliances.

Yep, that sounds sensible. I sometimes use consumer reports in my usual method for buying something in product class X. My usual is: 
1) Check what's recommended on forums/subreddits who care about the quality of X. 
2) Compare the rating distribution of an instance of X to other members of X. 
3) Check high quality reviews. This either requires finding someone you trust to do this, or looking at things like consumer reports.