How much should reviewers care about other things than an article's content?
I think the gut feeling is helpful during the evaluation process - one can probably not fight it anyway, so I think one should just accept that it is there. However, the gut feeling must not hinder a review based on the content of the paper.

So, what should not happen is, e.g.:


Stop reading after a few pages because you don't like the look, typesetting, language, variable names… (you may, however, stop reading if the style hinders your understanding, which is something completely different). Even if you hate Times New Roman or Arial, be professional and keep reading. 
Keep worrying about issues as above when it comes to write the comments (with the exception of the language, but I am always very careful about comments on language). Comments should mostly address the content of the paper, especially your recommendation should not be influenced by gut feeling. So once you read everything carefully, form an opinion not based on the look of the paper, but on the content (which you have digested at that point and hence, you should be able to evaluate it without taking the look into account).


One exception is figures: If figures are poorly formatted and don't allow to extract the information, this is a serious issue (too small font, pixel graphics with poor resolution, colors that are indistinguishable for common color blindness…). But also here it is more about "can I extract the information" and not about "do I like the look".

Be extra careful with gut feeling if you review something which is borderline for you field. As can be seen in the above comments, the styles of submission vary greatly between fields (extreme example: Some field have all floats, i.e. tables and figures and such, on extra pages at the end of the documents, other field have submission that basically look like a final article, some fields use double spacing, some don't…).