It's as good of an appointment as we could have hoped for.
It's not another heel turn in playing style. It won't require us to rip up any good work that has been done over the last couple of years. He has the long-term vision and desired playing style that people admired about Puel, but he has a better record of actually achieving that style in the Premier League. He will create a much stronger bond with the players, fans and media. He will offer a fresh, exciting new era when we most desperately need something like that to unite a disgruntled and divided fanbase.
He is admired and respected in the game. He is a thorough manager that is studious towards the game. I posted this before, but this is from the excellent book The Mixer by Michael Cox:
"Stylistically, Rodgers is the most 'foreign' British manager the Premier League has seen. His professional playing career ended at 20 because of a congenital knee condition, but Rodgers was determined to make a serious impact on British football. 'My ideology was, "OK, I'm not going to have an influence on the game as a player, technically or tactically. Can I do it as a coach?" My objective was to show that British players could play football.' Rodgers particularly admired the Spanish model, long before their dominance at international level, and spent extended periods in that country furthering his coaching education. His ideal weekend involved flying into Barcelona on a Saturday evening, spending the Sunday watching Barga's youth matches, heading to the Nou Camp to observe the first team, then flying home. He visited the training grounds of Valencia, Sevilla and Betis, always pinpointing clubs who emphasised a long-term, possession-based, collective football style and regularly promoted youth products - in other words, he didn't bother with Real Madrid. He took Spanish lessons for seven years, conscious that a move to Spain might suit his coaching career, and he also paid close attention to the likes of Ajax and FC Twente in the Netherlands."
The negativity seems to centre around the Brentishness of his interviews and the fact anyone could win things at Celtic. The first is irrelevant and the second isn't a negative. Winning things is never a negative, no matter how easy people deem it to be.