Professors claim that I will never be accepted into a decent pure math graduate program because my university isn't strong in pure math... How much of this is true?

Context: When I was 12 years old, I skipped the rest of middle and high school and jumped right into community college. At 16, I ended up with a high school equivalency, an associates degree, approximately 70 college-level credits, and 30 high school-level credits. While searching for universities to transfer to as a math major, many of them categorized my entire time at community college as high school since I got the high school equivalency and associates degree at the same place, and would've took me in as a Freshman. If I had done this, I would've had to retake dozens of classes that I already passed with flying colors: 2 semesters of English, 3 semesters of History, 2 semesters of Chemistry, Calculus I, II, III, differential equations, and so much more. I would understand if they rejected these credits if I did poorly in the classes. However, I got A's in almost every class with 3.88 GPA, and found it ridiculous to have to take them all again. A relatively prestigious yet heavily applied university relatively close to where I live accepted my application, let me transfer 66 of my credits, and offered me decent financial aid, so my stupid 16 year old self accepted their offer and began attending as a Junior. Despite being an applied math school, I was able to take most of the main pure math courses: 2 semesters abstract algebra, 2 semesters analysis, topology, 2 upper logic classes, number theory, and a few applied math courses. My GPA is 3.82 with mass classes being 3.84. Unfortunately, I have no research experience. I tried applying for over 10 REUs this summer with no success. I also am unsure whether I will do well on the GRE or not; I am taking 20 credits this semester, making it difficult to find time to study for it, and also somewhat struggle with timed tests. In terms of specific interests, I enjoyed pretty much all of the math classes I took so far, but am particularly fond of algebra-related subjects, and also foundations like logic and category theory. Now 18, I am getting ready to apply for graduate school (edit: to be clear, I graduate this semester despite being a fall semester). Today, two of my professors were telling me how I'd never be accepted into a decent pure math graduate program because decent pure math schools exist in a kind of bubble that only accept students from other schools strong in pure math. They discouraged me from applying to less prestigious schools, such as state schools, explaining how the research they do is "generalizing theorems that nobody cares about to begin with", and that I would never be able to get a job from a PhD in them. They encouraged me to apply for applied math programs, and to be very vague about my interests in my personal statement so that they don't figure out I'm mostly interested in pure math. They said I might be able to find some type of applied math adjacent to the math I really want to study. I know they are all applied mathematicians and might be biased, so I wanted to check if anyone here knows how much of what they said is true and if you have any advice?