The Rama (OC 142:1) rules that a mistake which changes the meaning must be corrected, while [mere] changes to the vowels or trop should [post-facto] only be complained about.
The Mishna Berura there clarifies that the Rama is using vowels and trop as examples of things which don't change the meaning because they usually don't, but if they did then they would be fully correctable. (This interpretaion likely seems obvious for vowels (eg. חָלָב and חֵלֶב) and the Rama presents vowels and trop together, so the extension is highly plausible.) I don't know of anyone who argues on this.
(Interestingly, the Mishna Berura is quoting the Shulchan Atzei Shittim whose example of a mistake that changes the meaning is reading a conjunctive trop instead of a disjunctive trop. While it may seem that he means any such switch, it's hard to see why, for example, reading Vayomer with a Merkha in Genesis 15:7, even if non-standard, would change the meaning. One generally needs to pay very close attention to catch some of these.)
Consider this example of switching a Merkha and a Tipcha (Isaiah 42:19 (Haftarah for Bereishit)):
מִ֤י עִוֵּר֙ כִּמְשֻׁלָּ֔ם וְעִוֵּ֖ר כְּעֶ֥בֶד יְהוָֽה
who is blind as he that is wholehearted, and blind as the LORD'S servant?
מִ֤י עִוֵּר֙ כִּמְשֻׁלָּ֔ם וְעִוֵּ֥ר כְּעֶ֖בֶד יְהוָֽה
Who is Blind as He Who is wholehearted, and Blind as a slave is the LORD.
Or this of shifting the Etnachta by one word/phrase (Leviticus 21:9 (Weekday reading of Emor)):
וּבַת֙ אִ֣ישׁ כֹּהֵ֔ן כִּ֥י תֵחֵ֖ל לִזְנ֑וֹת אֶת־אָבִ֨יהָ֙ הִ֣יא מְחַלֶּ֔לֶת בָּאֵ֖שׁ תִּשָּׂרֵֽף
And the daughter of a priest, if she profane herself by prostituting: she has profaned her father; she shall be burnt with fire.
וּבַת֙ אִ֣ישׁ כֹּהֵ֔ן כִּ֥י תֵחֵ֖ל לִזְנ֣וֹת אֶת־אָבִ֑יהָ הִ֣יא מְחַלֶּ֔לֶת בָּאֵ֖שׁ תִּשָּׂרֵֽף
And the daughter of a priest, if she profane herself by prostituting her father: she is profaning; she shall be burnt with fire.
(Yes, both of these mistakes actually happened. cringe)
For an example where just changing the level of disjunct matters, consider (Exodus 21:36):
א֣וֹ נוֹדַ֗ע כִּ֠י שׁ֣וֹר נַגָּ֥ח הוּא֙ מִתְּמ֣וֹל שִׁלְשֹׁ֔ם וְלֹ֥א יִשְׁמְרֶ֖נּוּ בְּעָלָ֑יו שַׁלֵּ֨ם יְשַׁלֵּ֥ם שׁוֹר֙ תַּ֣חַת הַשּׁ֔וֹר וְהַמֵּ֖ת יִֽהְיֶה־לּֽוֹ
but read with a Pazer on the second word: א֣וֹ נוֹדַ֡ע. Every word is still disjunctive or conjunctive as before, but the meaning changed from knowing it was an ox who had gored in the last few days to knowing in the last few days that it was an ox who had gored. Big difference: how much warning does the owner need? (If I notice a more striking example I plan to edit this.)