PSN81, why don't you do the experiment, since you already have the lube. Then let us all know how it performed.
I'm all for experimentation. I've tried a lot of different lubes over the years, looking for the "best". I've come to the conclusion there is no "best" lube. And there are no magic lubes.
This is a great way to start an argument. There are some folks who believe their way is the best and only way, and if you're doing something different, then your wife is ugly and your kids are stupid.
In that spirit, here is my way.
Drag washers and gears get either Shimano drag grease or Cal's drag grease. I have both and can't tell the difference, in use. I use the same grease for both drags and gears because if there is going to be any cross contamination, this is the place for it to occur.
Spool bearing get TSI321 I've tried everything I could find for this application, and TSI321 gives me what I'm looking for in a spool bearing lube. If you're one of those folks who service your reel once per year no matter what, this might be the lube for you. If you use any of the very light, low viscosity bearings lubes; such as rocket fuel, once per year is not often enough. Yopu need something heavier, or need to apply a lot more often. TSI solves that problem; giving me the high speed performance of a very light oil, but will last all summer.
Other bearings get 90wt gear oil. I used to grease all frame bearings, but getting them clean while servicing either takes a long, long time, and an ultrasonic cleaning unit. Gear oil gives almost the same smooth feel and cleans up a lot quicker and easier.
The levelwind is the most problematic part of a baitcast reel. It's a worm gear, exposed to the elements. If you grease it, grit will stick to the grease, and work it's way into the gear, causing wear. Ditto if you use gear oil. If you use light oil it will wash out fairly quickly; again, causing wear.
I've been using TSI321 on all levelwind components for the last three years, with excellent results.
Any sliding parts, like the clutch mechanism, get TSI321.
So to answer the original question; Cal's and Shimano grease are both made for reels. TSI and 90wt gear oil are not.
Lube is lube, and there's nothing that says gease or oil nor specifically labelled for fishing reels won't work just fine. An example that comes to mind is what's known as spindle oil. If you have a machine shop nearby, see if they will give you a small sample. It's only sold in bulk quantities. I used this stuff for years as spool bearing lube. It was a nice compromise. Thin enough to give good casting performance, and longer lasting.
Granted, there will be application specific issues. You would not want to pack your spool bearings with grease, and you wouldn't want to use light weight bearing oil on your gears, but a little common sense can guide you.