The meaning description for 変える seems to be contradicting itself. The first paragraph says it’s about “changing one thing for a similar thing”, but the second paragraph says it means “altering the nature or state of something” while 代える means “exchange one thing for another”. Which is correct?
the way i understood it might be different to how you’re interpreting it: in my reading 変える is more about alteration while 代える is more about replacement.
in case that’s not confusing enough, in later levels you’ll have at least two more kanji for the verb かえる, and arguably a couple more as well 
(帰る and 返る are a bit further afield in terms of definition and the okurigana are different, but they are homophones lol)
Hello!
“Altering the nature or state of something” is closer to the meaning that 変える is usually used for. I think that the bit about "changing one thing for a similar thing” is just to try to play on the Kanji 変 meaning “change” and is meant to be used for the mnemonic/memorizing the overall meaning, rather than the nuance.
Based on the text from the 変える page:
The kanji is change, and this verb is to change something. If you change one thing for another thing, you are going to change it, after all. This word refers to changing one thing for a similar thing.
変える and 代える sound the same and are sometimes used in similar contexts, but are different in nuance. 変える refers to the act of making something different, and involves altering the nature or state of something. For example, changing the layout of a room or changing one’s perspective on an issue. 代える means to substitute or exchange one thing for another that is expected to fulfill the same role, use or purpose, such as replacing a worker with a substitute.
Essentially, the first paragraph seems to be meant to help you memorize the basic meaning. The second paragraph is the more accurate nuance/usage. If you look at other compounds 変 is in you can see that they mostly lean more towards the “altering the nature or state of something” meaning.
However, it could also be argued that in certain contexts it is close to “changing one thing for a similar thing,” as I’ve seen 変える used in sentences like "He changed his hair color,” “I think I will change jobs,” and “Do I need to change my diet?” In this case, it is kind of similar to “changing one thing for a similar thing,” and is still clearly different from “exchange one thing for another.” Perhaps if “to” was used instead of “for” that would be clearer?
The four かえる’s can get kind of confusing in their specifics at first (変える・代える・換える・替える), but they become clearer over time.
Also, if you’re ever concerned about nuance I highly recommend looking at websites that have example sentences so you can get a clearer vibe! Websites like immersionkit pull sentences from anime or Tateoba which is a massive, crowdsourced database of example sentences (with translations).
Thank you for the thorough explanation of the nuance. Very helpful 
That said, I don’t really see a reason why the first paragraph has to confuse the matter. There nothing about the kanji that would make “replace” change work better than “make something different” change as a mnemonic. It’s just teaching the wrong nuance.
in my reading 変える is more about alteration while 代える is more about replacement.
Yes, it would seem this is correct and what the second part of the meaning explanation says, but the first part says the opposite. Thus my confusion.
I still think it is possible to read the first paragraph the way you are but not necessary to.
As a general rule, this part of the card must make use of the kanji’s meaning labels in order to introduce the word’s meaning label. Generally these first couple sentences are very contrived and in many cases run counter to the nuance of the meaning in order to strike a more memorable connection.
A very common construction involving 代わる is 代りに, which means substituting something for something else:
自分で行く代わりに、彼は息子をその政治集会に参加させた
Instead of going himself, he sent his son to the political meeting.
私はドイツ語の代わりにフランス語を勉強した。
I learned French instead of German.
私は君の代わりに手紙を書いてもいいですよ。
I can write the letter for (instead of) you
I think it conveys the nuance of the word fairly well. It’s about switching something for something else, not changing the nature of something else which is what 変 is usually about.