Suppose you're in some low limit, no fold'em hold 'em game, say 10-20 or lower, and you're on the button or cutoff. The game has a $5 rake (usually plus a customary $1 toke). Everyone folds to you. Should you attempt a steal raise, and if so, with what cards?

You said they're not folding so only value raise.

Yes, you should have an open raise range defined for this scenario.

This is best illustrated by extremes. Would you fold or limp with AA in this scenario?

Should you raise or limp with 72o in this scenario?

What you stop raising with is somewhere in between based on your predefined range adjusted for current players. Based on the players, I may tighten or widen the range. This also changes if the table has gone short. As a rule of thumb, I don't raise with 'junk', whatever you define that to be. As for me, if I am raising in that scenario it is with a playable hand.

Rake has nothing to do with it IMO.

You would raise the same hands with a fixed rake of 2BB/hand and 0.2BB/hand (no flop, no drop)?

I think opening ranges are heavily dependent on rake, particularly in limit holdem because the pot grows linearly as opposed to geometrically, as it does in no limit. There's a certain cap on potential winrates in limit games because of this effect. Usually it's around 1 or 2 big bets per hour depending on rake and how bad your opponents are. In some cases, like 2/4 or 3/6 limit holdem, your best opponent is the rake and if you can beat it, it's for less than 1 big bet an hour. That's a big if.

All that said, I suggest you raise this range on the button for now vs typical loose passive opponents:

44+, A2s+, A8o+, K6s+, KTo+, Q9s+, QTo+, J9s+, JTo, T8s+, 97s+, 87s, 65s.

Then once you memorize and apply that range, you'll notice spots to loosen up. Maybe a tight guy happens to sit to your left in the small blind, but there's a really bad player in the big blind. I'd loosen up significantly from the above range in that spot because there's a huge difference between heads up and 3 way poker. Heads up with a strong range vs someone playing 52o for a raise in the big blind? You're going to make tons of dominating pairs that you can either bet bet check with, or bet bet bet with. Those should be your primary lines vs loose passive opponents.

Then once you get good at turn and river betting, you can loosen up with the more showdownable hands first, like 22, 33, A5o+, K9o, etc.

It's important to note that this range is a product of a few different variables:

your skill level postflop

the rake

your opponent's preflop folding frequency

The first two are somewhat self explanatory. The last one may need some explaining:

When three good players play their respective positions in a 3 handed situation, the button's ev sources look like this:

button = earns profit from raising hands that are profitable to play and folding those that are not. They don't, however, get the whole pot in the long run with rare exceptions, such as but not limited to holding KK, AA, or AKs, in which cases the button will earn (small blind + big blind + postflop profits). For other, weaker starting hands, the button will win just a fraction of the blinds. This fraction is equal to the sum of the negative winrates that the players in the blinds will experience. Some of the weakest hands to earn a profit, such as but not limited to J9o, T8o, T9o, are actually unprofitable when they get action from a blind. This is because in a tough game, fold equity preflop makes these hands profitable.

Contradictory Holdem sounds too confusing for me. :/
If the blinds are truly never folding, you could just raise something like TT+/AQ+, limp a bunch of other playable hands and do pretty well by never bluffing post-flop.

Suppose the game were loose aggressive [sometimes it is]. How would you change these ranges?

Tighten up and do stoves to get a general idea of how wider ranges allow you to get more value with strong hands, draw at good odds, and fold at bad odds. Notice that there's a difference between these situations:

5 limpers then button raises and everyone calls.

Utg raises then every one calls