I am less convinced that Clinton personally is as committed neoliberalism as she was before the 2008 recession and the Wall St. freak out over even modest reforms. But it is certainly the case that these are the conflicts in philosophy that drive the vehement vitriol on either side of the campaign. Progressives view Clinton's legislative record as Senator form NY and her publc statements as FLOTUS as being part of the overall neoliberal philosophy that has created a revolving door between Wall St and Washington. Things like Hillarycare and CHIP are regarded as not sufficient to address the reality that it is the existing system of financial and business regulation that creates the social and income inequality that drives what is wrng with America.
For Clinton supprters who regard themselves as centrists, this is what makes Sanders not merely crazy, but dangerous. If you believe that future economic growth and general ecnomic prosperity depend on minimizing the burdens on capital markets, business formation, and other "free market" values, Sanders assertion that markets cannot be trusted and inherently produce inequality (unless regulated) threatens to undermine the whole future of the economy.
This also, incidentally, is one of the contributing factors to the "do you focus on economic inequality v. racial inequality/gender inequality." The argument of socialists (and economic progressives) since the 19th Century is that it is the economic inequality that reenfrces racial and gender inequality. It is therefore impossible to genuinely address issues of racial and gender inequality in any meanigful way without addressing the overall economic inequality. Neo-liberals are ideologically wedded to the conclusion that racial and gender inequality are distinct and *must* be addressed seperately. (I say "ideologically wedded" because, as discussed above, neoliberalism views unregulated capitalism as inherently positive, with regulation needed only to address market failure and consumer protection. By contrast, economic progressivism can be quite racist and sexist. Huey Long, for example, was an economic progressive to the left of FDR and a total racist.)
As with all stark philosphical schools, you will find a range of folks and plenty of "yes, but . . ." arguments. You will also find lots of folks in the electrate who don't fit either philosophy and like a candidate for an unrelated reason ("Honesty," "gets things done," "cares about people like me," etc.) But the article linked to above is extremely useful in understanding why so many people who are eyeball deep in the policy fights care so deeply and vehemently about the election outcome.