Can you kayak fish the larger bodies of water in the Stonebridge community in McKinney? Or even fish them in general?

Hahaha!
No*

You can bank fish if you are a resident of the neighborhood.
There is now an HOA ordinance against vessels and wading in bodies of water in Stonebridge.

Now, if you happen to be married into or are very good friends with the family that owns the business park at the big lake, you may or may not have kayak fished the big lake before the church was constructed and prior to all the plots being built out 8-9 years ago

It is pretty standard for North Dallas Suburbs to outlaw boats and swimming in their neighborhood ponds. They claim it's a safety issue preventing unsupervised kids from having to be rescued by the Fire Department. The people who pay an extra $50,000 or more for a pond view lot don't want it to become the after school and weekend hangout for kids with their pool rafts and snorkeling gear. If they allowed it, my son would be the first one in.

Yea, that'll be a no I bet!

Regarding the bank fishing, there are signs everywhere requiring a Stonebridge Resident ID. They do have a hatchery program in place and most of the lakes /ponds in the area are well maintained, so that's probably why they restrict fishing to residents only.