This is not an answer that stems from vast cosmological knowledge and experience, but from an intuitive mathematical understanding of stochasticity. I would point out that stars do not have the visual appearance of stability or a predictable nature. They are churning, belching balls of nuclear plasma. On a macroscopic scale, I would expect stability to look like smoother surfaces or uniform activity. Any object that you might describe as "constantly exploding" or even "on fire", or particularly, "undergoing nuclear reaction", I would ordinarily say involves an element of chance.
The flare and CME activity of our Sun is governed by a roughly 11 year cycle. But it's not exactly old faithful. The activity of the Sun follows patterns, but they are noisy patterns. However, even though stars are the very image of chaos to our view, it seems that they are actually quite predictable. One reason is that they live in a vacuum. Literally. Or very near a vacuum. Particularly since your question eliminates consideration of external interactions, we are talking about stars like ours, surrended by mostly a lot of nothing. So when plasma erupts out of the star at less than escape velocity, we know that ultimately that plasma is coming right back home to the star. It's not going to smear onto some other object. And the goop from other objects isn't going to smear onto the star.
Second, the time-scale of a star's evolution is enormous. Imagine watching a timelapse movie of our Sun where each frame of the movie shows the average (mean) appearance of the sun over 100 eleven-year solar cycles. Now you would see something that looks quite smooth, stable. And you could watch that movie of a stable glowing ball all day long without seeing any dramatic change. (Assuming 24 frames per second, watching the movie all day long would take you through 2.3 billion years of the Sun's life.) Because the timescale in question is so long, the bubbling, churning, and exploding we see on our timescale amounts to unfathomably insignificant blips in a stable, predictable, burn process.
In general, any stochastic (random) event reproduced enough times, in the same way (with the same kind of randomness), will lead to stable, predictable outcomes. A man has solar panels on his roof. Some days are sunny, and some are overcast. Some days the panels get covered up completely in snow. But over the course of a year, we can still predict approximately how much power his panels will produce with about 98% accuracy, assuming there is no external influence, like the house burning down.
So yes, excluding external interactions, if you know the total mass and composition of a star at conception, it makes sense that the chaos and noise of the atomic fireball would have a net zero effect on the outcome.