MIMF

I just started looking at building pickups. When I did a little digging about Alnico Magnets, it appears you can demagnetize or change their magnetic strength if you put them next to another magnetic field.
I have a few sets of pickups that I put into zip-lock bags and threw them into the same drawer.
Did I just change their characteristics? That would be a major bummer. I never thought I have to worry how I store the pickups.

Alnico V is pretty resistant, I certainly wouldn't worry about it unless you notice low output on individual strings. If you suspect the Gauss is lower you can recharge them using a couple of rare earth magnets.

What would the procedure be for recharging the individual poles using a rare earth magnet? Do I have to take the pickup apart?

It depends on the pickup. Fender style pickups can be recharged in the raw or with the covers on.
Humbuckers are very unlikely to get discharged but they would need to be disassembled to be recharged effectively.
For individual pole magnets I recharge them one at a time using two stacks of 6mm or 1/4" dia N52 round neodymiums both top and bottom. I pull them off and let them click back on the ends of the pickup magnet simultaneously several times for each rod. Most folks will use larger blocks of Ndym but these are very dangerous if you don't have a fixture to hold them in alignment and keep them from shattering into each other. They are extremely brittle and can literally explode not to mention the pinches and blood blisters they can cause.