I have a double major myself from a small liberal arts college and have worked in tech software startups my entire career. From an academic and experience standpoint I would not change it for anything. However, the environment today (mostly in Silicon Valley) tends to be somewhat pedigree biased towards a handful of top schools.
This is especially true for hiring recent grads right out of school. I can’t tell you how many hiring meetings I have been in, or recruiters that call me, where they all point out that this person went to Stanford, MIT, Berkeley, Carnegie Mellon, CalTech, etc.
I am not saying I agree with that, but it can make a difference.