Mixing Adidas with Nike is known as one of the biggest style 'law breakers' in the fashion world. I agree to some point. I mean I don't like mixing the 2 brands' logos in the same outfit. It doesn't look good and you can't make it look good, not even for the ones who possess major styling skills.
Anyhow, I think it's fully acceptable as long as you can't see the logos (Example below.) I'm styling my favourite Adidas shorts with my distressed cropped Nike sweater. And yeah it looks real good. As long as you can't see their signature logo on one of the pieces, I think it's totally fine.
Distressed Cropped Nike sweater - Nike (similar)
Adidas Originals Leather Shorts - Adidas (similar)