The search field should find titles and such without regard to marks. For non-English words it makes MusicBee hard to use.
For example, let's say I want to find all songs by "Maria Bethânia" (an all-time popular singer of Brazilian roots samba). If I type "maria bethania", nothing comes up; I have to make sure I type "maria bethânia", with the accent (which of course would miss any songs if someone accidentally left the accent off on a song's metadata).
Similarly if I want to find all songs in the genre forró (a popular style of music from the Brazil Northeast), I can't type "forro", I have to type "forró".
MusicBee already searches without regard to case. It should search without regard to marks as well. (MediaMonkey does this correctly, for example.) Doing so is no mystery; it is completely laid out in the Unicode specs; see UTS #10 § 1.1
Another more efficient approach is to store special search fields in the database already normalized to NFD for example, with the separate mark characters removed. Perform the same normalization on the search text, and then you can efficiently compare the characters without worrying about case or marks. See UAX #15 § 1.2
However you do this, it needs to be fixed. MusicBee shouldn't assume everyone using it is am American listening to music with only ASCII characters in the metadata.