We all know Bostonians pronounce words differently than Houstonians. Do you say "Where are you all going?" Or "Where are y'all headed?"
I grew up in Nevada, but when I lived in Texas, I learned a lot of new pronunciations. At Thanksgiving, most native Texans say turkey and all the "fixins" not "fixings" or even "sides." My daughter pointed out that I say, the days of the week as (e.g., Monday as "Mon-dee, Tues-dee" instead of "Mon-day, Tues-day").
In an article on the subject, James Joyner notes, "I say “loyer,” not “law-yer,” despite the latter pronunciation dominating the places I’ve mostly lived. Ditto “may-uh-naze” rather than “man-aze.”
So then, if I have a rhyme about the "sea" and planned to rhyme it with "Thurs-dee" I'd have a problem. A reader in another geographical area would think the rhyme was broken or just wrong. I love to play with rhyming texts, but it is something to think about when tempted to rhyme the next picture book story.