Actually, a working ABM system makes a first strike more unlikely, even in a Soviet-style "rational actor" situation.

The strategic purpose of a first strike is to take out as many of the enemy's missiles and retaliatory capacity as possible, while leaving a sufficient force of your own for additional attacks. Only an idiot would expend all their missiles on a first strike, or waste them on civilian targets like cities. An ideal first strike also includes attack submarines, but that's another story.

You set up the targeting, make decisions based on the hardness of the targets, and go from there. In the absence of defences, the only variables are the reliability of your own missiles and targeting systems, which can be calculated quite closely. Hard targets can take multiple warheads to defeat, but you can count on almost every one going where it's supposed to go.

With an ABM system in place, of any kind, the calculations become very difficult. Theoretically, an ABM system will stop a certain percentage of your offensive missiles. In real life, you don't know which ones. All of your missiles might hit one target, while none of them might hit another one.

The outcome of a first strike becomes much more of an unknown with missile defence. And that tends to discourage such actions.

Now, if one side has an ABM system and the other doesn't, the ABM side has a much easier time with a first strike. The other side's missiles are helpless, and you have an ABM system that needs to defend only secondary targets.

The ideal is for both nations to have an effective system, and some people proposed the U.S. and Soviets cooperating on a system.