I'd like to install a frost free hydrant in my backyard 250ft from my house. My plan is to run 1" polyethylene pipe 4' underground from my basement (through the foundation) to the hydrant. I have a manabloc water manifold with 1/2" PEX pipe. Is there a way to connect the 1" black polyethylene to the 1/2" PEX inside my basement or will that limit my water pressure in the 1" pipe? Is there another solution other than connecting to the 3/4" PVC pipe connecting my well pump to my water manifold and hot water heater?

The issue isn't as much PRESSURE, but more so WATER VOLUME. Here, attaching a 1" pipe to a 1/2" pipe will reduce the volume of water available in terms gallons per minute to that 1" tubing. The distance you mention further aggravates things. Attach your 1" tubing to the 3/4" PVC pipe as that seems the best you can do here. Pressure will be pretty stable and volume (GPM) will be much greater than attaching to the 1/2" manifold.

Mark