The standard answer to your question is use the comma unless you don’t really need it:
In a sentence containing two or more independent clauses joined by a coordinating conjunction (and, but, or, nor, for, so, yet), put a comma before the conjunction. This is not a hard-and-fast rule; no comma is needed between two short independent clauses with no internal punctuation. — Kate L. Turabian, A Manual for Writers of Research Papers Theses, and Dissertations, 2013, 295.
A guide to business and professional writing takes the opposite approach — don’t use a comma unless you have to:
The comma before a coordinating conjunction that joins two independent clauses is optional in professional writing. If a comma helps the meaning or point of your sentence, use it. If a comma seems to create an unnecessary break, then don’t use it. — Paul MacRae, Business and Professional Writing: A Basic Guide, 2015.
The first guide is closely allied to the Chicago Manual of Style; the second supports its argument with a now dead link to a Canadian university. You decide. I suspect that were one to quiz the author of the business writing guide, his global permissiveness would likely reduce to the use of and, but not but or yet because of their contrastive nature.
Both guides agree that short independent clauses joined by a coordinating conjunction require no comma. How short is short is left to the writer.
18.09.2012 · You can read the entire Electronic Code of Federal Regulations Title 7 Part 205.236 (but you won't so I will summarize). — “How Long Does it Take to Become Organic: Organic Myths Part 1,” Zweber Family Farms.
Few would object to the lack of a comma before so, especially in such a short, parenthetical sentence. In practice, however, even in that context, but will take a comma:
21.09.2017 · I can't tell you what the shows will be about (well, I could, but I won't), but I will tell you a couple of things they WON'T be. — “Has George R.R. Martin Already Revealed the Subject of One Game of Thrones Spin-Off?” Vanity Fair
This would suggest that your first example would require a comma before but, but whether you put a comma before and in the second is up to you. To most speakers, there would also be a slight difference in meaning.
I learned to stop worrying and now I love the bomb.
No comma increases the topicality of now loving the bomb; with the comma, which would also be indicated in speech, there is more of a two-part process:
[First] I learned to stop worrying, and now I love the bomb.
As far as I know, following the comma advice of the guide based on the Chicago Manual has not yet been stigmatized as pedantic, like, say, insisting on never splitting infinitives even when the result is awkward. So I’m a bit puzzled about your concern.