Having a BA or BS in Chemistry shouldn’t matter at all. At U of Wisconsin-Madison, a forever top 10 grad program in Chemistry, the undergrad degree you get depends on which breadth requirements you may have or, if you qualify for both, which one you choose. There the credits required for the major is the same for BA or BS. Perhaps his school has different requirements, which I find strange as the major should have the same reqs. At UW the numbers of foreign language credits and more/less of the sciences/humanities/social sciences are different. I got an Honors BA in Chemistry from UW because I liked the white tassel more than the yellow- choice made just weeks before graduation. I met both BA and BS req and had plenty of chemistry. Went the medical route, however.
There is overlap in course content for chemistry and physics. Physical Chemistry required for a chemistry degree will cover many physics concepts. Taking the Physics versions of the same content will not help. Finding less time for more in depth courses in chemistry because of taking physics courses will not improve the knowledge base for Chemistry GREs or knowledge base for chemistry grad school.
Taking the bare minimum in any major is not great preparation for either jobs or grad school. Others with more passion for the field will be better prepared and hence more competitive for positions. He needs to choose one or the other- the field that most interests him and he does best in. Fence straddling will get him neither.
That is likely a school-specific question to the extent that aid provided by the school is involved (as opposed to federal or state aid). Both federal Pell grants and subsidized federal direct loans are limited to 12 semesters.
The differences between the BA and BS at universities that have two options vary widely. For example, Emory's chemistry department states that the major difference is really just physical chemistry - BS majors must take two semesters of physical chemistry with lab whereas BA majors must take one semester without a lab. Carnegie Mellon's BS offers 5 fewer courses in chemistry than their BA, mostly in physical chemistry. At Arizona State, the BS requires 46 hours in chemistry and 20 hours of cognate courses, whereas the BA requires 30 hours in chemistry and 16 hours of cognate courses.
And each university has a different recommendation. Emory says that students who want to work in chemistry should do the BS and students who want to double major or go onto non-chemistry grad school should do the BA. Carnegie Mellon says the BS is best for students who want graduate school and research positions, whereas the BA is recommended if you want to add breadth or depth in another area or go to less technical careers. ASU says that their BS is for grad-school bound folks whereas the BA might be more appropriate for those who want to go straight into the work force, and I’ve seen that said at a lot of colleges.
I know in my own field, psychology, some colleges offer the BA and the BS. The BS generally required more natural and physical sciences classes. But in psychology, only certain subfields valued that. Nobody cares if a social psychology hopeful knows a bunch of biology and chemistry, unless they plan on integrating that into their research.
In many cases, the BA is not the “watered down version.” The BA is simply the standard version with the core knowledge, whereas the BS is the enhanced version with extra depth or breadth.
Grad professors don't care, and probably won't even notice, the name of the degree you get - BS vs. BA. Instead, what they care about is the coursework you've done (and your research). Let's say that Student A elects to do a BA, decides halfway through junior year that she wants to go to graduate school, and completes all the coursework requirements for the BS but still gets a BA because of paperwork. Is she at a disadvantage against Student B with a BS and the identical course load? No, of course not.
Student A might even elect to do the BA deliberately because she wants to specialize in an area that the BS doesn’t allow her to - like let’s say the BS requires three semesters of physical chemistry when she knows that she wants to do research in organic, so instead of doing the BS, she choose the BA, takes 1-2 semesters of physical (or whatever the foundational minimum is for graduate school) and spends the other 1-2 classes remaining specializing in her research area. Or better yet, let’s say she uses the extra BA time to do a concentration in computer science or math because she wants to go into computational chemistry, or to earn a certificate in atmospheric science because she wants to study oceanic chemistry or something in grad school. She’s not necessarily at a disadvantage; in fact, for her field, she might be at an advantage instead.
The point is, the letters behind the name do not matter. What matters is the coursework, the foundation of knowledge. OP’s kid just needs to make sure that he takes the necessary coursework to get him into PhD programs, should that be the goal; if he can do that by opting for the BA, then it doesn’t matter. Consultation with professors in the know will answer the question of whether he can.
That Emory chemistry situation IS a significant difference. My UW situation involved other courses, the chemistry requirements were the same for a BA or BS. It won’t matter to grad schools or employers if you had 3 or 4 semesters of the same foreign language, took more or less of elective science, humanities or social sciences in addition to the ones needed for your major.
Some things to consider when choosing your school. Flexibility in majors, adding and changing majors. Being allowed to make changes after a certain time (could mean more semesters if later than sooner). College is so much more than the location or campus.
I once asked dh (who is a prof at a med school, but he has grad students as well as MD/PhD students in the lab). He doesn’t care about whether you have a BA or BS, he does care about whether you seem to understand your courses and research you have done. (A surprising number of students bomb the interview.) He has a BA in both physics and biology and went on to get his PhD in biophysics at Caltech. It was a long time ago, but obviously the double major didn’t hurt him. Your son’s professors can probably give him the best advice, but I’d lean toward him giving physics a whirl.