Well, I'll chime in since you hit my rhyming wheelhouse. (grin)
I have four picture books out, the last one coming out next spring, two fiction, two non fiction, all traditionally published, and all four are in rhyme.
I'd say overwhelmingly in both the PB and magazine market if a manuscript rhymes, editors want accentual syllabic verse. They do overlook a few scansion hops once an author is established and occasionally when it serves the story. But early on writers tend to be held to a much stricter rule.
The general feel in my experience (around 12 editors total in trade book and magazine houses like carus/highlights) has been either make your rhyme in flawless anapestic tetrameter, or iambic pentameter (or whatever your favorite meter is) or simply don't write in rhyme at all.
They would rather see a story in prose or lyrical free verse than accentual verse, which can be viewed as "improperly" stressed syllables done only to "make a rhyme work" or worse simply labeled as uncorrected errors on the writer's part. Eeek.
But I also need to say, from my writer's heart, that if you have a unique rhyme style that works for you and your story -- don't squash it just to fit the current zeitgeist/rules. Maybe it's the piece some editor will fall in love with. Brave, talented rule breakers can sometimes start wonderful new publishing trends
Hope the insight is useful.