"This book got me interested in Buddhism." Can I change this sentence to "This book made me interested in Buddhism." "This book got me thinking about my future." Can I change this sentence to "This book made me think about my future." If there are any differences in the nuance, could you explain it? "Get" is a very common word, but it's very difficult to use it properly. If I say "I got my car repaired.",I can also say "I had my car repaired." To me it seems to be much easier to use words other than "get". That's why I wondered if I use "make" instead of "get" in these sentences.
It's probably worth noting straight away that "to get" is increasingly common in OP's context. As this link shows, X got me interested in Y was virtually unknown a century ago, but it's now far more common than made me interested in.
But there are subtle syntactic and semantic differences. As noted above, of OP's first pair...
1: This book got me interested in Buddhism.
2: This book made me interested in Buddhism.
...#1 is more common, but both are acceptable. And so far as I'm concerned, they mean the same. But...
3: This book got me thinking about my future
4: This book made me think about my future
5: ✲This book made me thinking about my future (where ✲ marks a usage as unacceptable)
...with OP's second pair we can't just replace got with made. Notice also that we can explicitly use the "marked infinitive" (to think) with got (also to [present participle], but I don't know what to call that)...
6: This book got me to think about my future
7: ✲This book made me to think about my future
8: ?This book got me to thinking about my future (perhaps not everyone would accept this form)
9: ✲This book made me to thinking about my future
On the basic of the above, I suggest it's well worth learners spending some time becoming familiar with the syntactic possibilities of to get. Because it's increasingly common in modern speech, and can probably be used in more contexts than to make, it's likely to be more useful over the long term.
On the semantic front, note that to make often carries implications of deliberate and/or forceful actions. Thus with this pair...
10: He got me to eat snails in garlic butter
11: He made me eat snails in garlic butter
...there's a much stronger implication that in #10 he persuaded me (possibly quite easily). It would be quite reasonable for the utterance to continue with "...which I really enjoyed". But #11 implies he forced me (much against my will). That one might continue with "...which made me feel really queasy".