I agree that courses like cryptography are interesting and lie at the intersection of math and CS. I myself took that class during college (as a math major) and it was one of my favorites. That class is very self-contained. All the number theory and algebra you need will be taught in that class. But most of the math classes, like real analysis, abstract algebra, and topology, will be useless to pretty much anyone doing CS. There’s just no chance a grad committee will be upset because you don’t know how to use the Sylow theorems to show that every group of order p^2q (p, q prime) is not simple, or how to prove the Dominated Convergence Theorem. If you need some area of math for your CS research, you will be able to pick up a book and learn whatever you need to know at that time.
For example, in calculus, you learn the extreme value theorem: a continuous function defined on a closed interval [a, b] attains a max and min (thus you check the endpoints and find the critical points for the interior of the domain). In multi-dimensional calculus, you learn the extreme value theorem also holds for domains like [a1, b1] x a2, b2. If you study real analysis or topology, you will learn that the EVT holds for a continuous function on any compact domain. You will also learn the Heine-Borel theorem: compact if and only if closed and bounded (which holds for certain classes of metric spaces, including R^n). Every mathematician knows this theorem, but no teacher will ever mention that the EVT is really a statement about continuous functions defined on compact subsets of R^n to CS students, or to anyone else taking a basic calculus sequence. All they will mention is what’s known as the “closed interval method.”
I realize some schools may be impressed by a strong Math Subject GRE score (I myself took the Math GRE for my CS applications, and I’m interested in theory, but I also had already majored in Math and had been to grad school for Math so the test was pretty basic for me with essentially no dedicated preparation for the exam), and you’ll need to know this stuff to do well on that test. But some of those schools’ pages are out of date (one of the ones you linked to also mentions the CS GRE, which was discontinued 2 years ago). More importantly, your time can be better spent focusing on research or programming projects.
Nobody on adcoms will have a problem with you doing a 2nd major, unless it brings your GPA down, or gets in the way of your research (which is a real possibility). But doing a Ph.D. is about focus, not about being a jack of all trades (and master of none).
Like I said, it’s great to have all these ideas about your future, but just go to UCB and start taking Math 1A/1B/53 (depending on how much Calculus you have from high school), Math55, and CS61A/B/C, make some friends, and have some fun in college. After your first year or two, it’ll be clear what you want to major in. Then focus on that. When I was in college, I met tons of freshmen every year who came in thinking they’d be some Math+CS+Physics triple major. Hearing this over and over again got old quickly. Pretty much every single one of them just majored in one subject.
Based on personal observation, most people who take Math and CS classes do well in one and really struggle in the other. Most math students will struggle in classes like Computer Organization and Operating Systems because they’re so low-level and almost like engineering classes (but they’ll do well in classes like algorithms). Most CS students will struggle in algebra, analysis, and topology because they really don’t appreciate pure math (but they’ll do well in classes like crypto, dynamical systems, probability, etc.). When I took complex analysis, there were tons of engineers who could do the calculus computations, but got stuck on things as simple as combining de Moivre’s formula with the binomial theorem. Heck, tons of CS students struggle mightily with calculus and can’t even get an A in Calculus II.
That said, my algorithms professor did have a bunch of algebraic topology books in his office, so there are some people who really like both areas. If you end up loving the calculus sequence and you go on to take algebra and analysis, and you do well in them and enjoy them, then that’s great. But just take your life one step at a time.