This is a question about dialects placed under the umbrella of "Mandarin", not languages which are considered separate from Mandarin like Cantonese or Wu.
Wikipedia says that "Southwest Mandarin is about 50% mutually intelligible with Standard Chinese." which makes it sound like a completely different language from northern dialects. https://en.wikipedia.org/wiki/Southwestern_Mandarin
So, of the different dialects of Mandarin, (of which Wikipedia lists the following: Northeastern, Beijing, Ji–Lu, Jiao–Liao, Lower Yangtze, Central Plains, Lan–Yin, Southwestern, Jin, and Huizhou), which of these would a speaker of Standard Chinese actually be able to understand? Also, I am talking about speakers of these dialects actually speaking these dialects, not codeswitching to Standard Chinese so that a speaker of Standard Chinese could understand them, as I am aware many speakers can do.