Is a 2-way ANOVA immune to Simpson's Paradox? Sometimes continuous data is of the type that would result in Simpson's Paradox findings if groups were simply aggregated.  (See, for example, "Example #2: Baseball" on this page https://www.kdnuggets.com/2020/09/simpsons-paradox.html.)
In that type of situation, would analyzing the data using a 2-way ANOVA always avoid the spurious finding?  In the baseball example, would the paradox effect simply be seen as a year effect and the player effect would be correctly seen?

Simpson's Paradox can be seen in patterns among categorical variables (contingency tables) or continuous/scalar variables (which graphically would involve scatter plots with groups denoted by color, and might be referred to as Lord's Paradox).
Your query taps into the idea of whether you can mix the types of variables.  And, as Sextus Empiricus's answer indicates, the answer is yes...this is indeed possible.
However, the key to remember with Simpson's Paradox (and all the similar variations) is that the Paradox is a warning to explore the data more completely.  My reading of Simpson's reflections on this (and others who have thought more deeply about this) is that the answer is always "maybe".  On its own, it could be a player effect, a year effect, both or neither.  The advantage to the 2-way ANOVA is that you have the interaction term.  And while you could use the significance of these interaction to decide if there is or is not a scenario that leads to a possible example of Simpson's paradox, the underlying issue still remains...perhaps there is yet a 4th variable that explains the relationship in the dependent variable better than the currently available independent variables.  (And, I believe this is what Simpson intended us to attend to when drawing conclusions from data.)
