When does my opponent receive priority? It's the beginning of my turn; I draw a card and decide to go straight into combat. Can my opponent tap my creatures before declaring attackers with Gideon's Lawkeeper? Even though I didn't take any actions before declaring them as attackers meaning he never got priority before?
Yes, your opponent gains priority and has several opportunities to activate their Gideon's Lawkeeper.
Your opponent will get priority and may activate their Lawkeeper in your Upkeep, Draw, 1st Main, and Beginning of Combat steps. You cannot skip any of those steps. If you draw your card for turn and go straight to combat you're proposing a shortcut, but your opponent is not obliged to accept that shortcut. They can stop you at any time they would receive priority and cast instants or activate abilities.
Miles is right, but to explain in more detail.
Each phase the acting player gets priority. They either take an action or pass priority. If they take an action they get priority again with that action on the stack.
As soon as they pass priority their opponent gets priority and can act.
As soon as both players pass priority the top of the stack takes affect or if the stack is empty the phase ends.
If the acting player (you in this example) passes priority and your opponent then passes priority you can't change your mind. Unless they act that is the end of the phase. This means for example that you can't wait to see whether they tap anything before casting a spell. If you say "go" and they don't act then the turn proceeds to the combat phase.
So you can see that in this case, you draw a card and then try to go straight to combat in fact you just passed priority multiple times. Your opponent can accept that shortcut and the "declare attackers combat step" starts or they can interrupt at any point with an action of their own after you passed priority.
Once they have acted though that then gives you the option to change your mind and act anyway.
For example the following is legal:
- You: Go to attack (this is a shortcut saying you are passing priority until you get to the declare attackers phase)
- Them: I use Lawkeeper to tap your creatures in beginning of combat.
- You: Lawkeeper resolves (tap your creatures). Note that you are no longer in your main phase so cannot summon creatures or cast sorcery spells. If on the other hand your opponent had intervened in your first main phase you would be able to.
- Still you: Still in beginning of combat, I untap my creatures with X.
- Them: resolves
- You: Go to combat
At this point you passed priority, they acted with their priority and passed it back to you. You then acted again and passed it back.
They can now try to do something else but if they don't respond then declare attacker happens.