I fish an old 15 foot fiberglass boat.  It only has a 30lb thrust trolling motor as the main motor was long since removed.  It works fine for the lake I fish which has a 10hp motor limit anyway.   My question is that many time it seems the rear of the boat won't stay in line with the front and I sort of crab walk down the lake.   Not so much when under full power but mostly when on and off the motor and especially if there is about a 5mph+ breeze going.      Was wondering if the lack of the rear motor in the water acting like a rudder could be the issue?    I notice most pros fish with the motor tilted down unless really shallow water.

my old jon boat did that if the outboard was not in the water.

my current bass boat does not do it at all . a lot of it depends on the boat.

if there is no weight on the back, wind will push it around a lot more.

Without the motor on the back working as a skeg/rudder, you will need to add one.  You can make one out of most anything that will stick down in the water about a foot deep and 10" wide.  Have it so you can tilt it up when in shallow water.  Also, try to balance the weight in the boat.  If there's no weight in the rear, it's going around.  Same as if all the weight is in the rear, the front is going around.