Hey Barry, you are right to ask this question. It should be 'fewer' because 'activities' are plural. However, yes, many native speakers make this mistake.

'Fewer' is correct. Native speakers do make mistakes like this if they intend to say something else and changed their mind, or if their English isn't good. But generally, no. Not in this country, at least.

‘To plan’ pairs with the countable form of activity, so ‘fewer activities’ is correct. ‘Less activities’ coming from a native speaker here would sound wrong but not surprising. ‘Activity’ has an uncountable form and in that case ‘less activity’ is correct. I planned 5 activities. (Countable) Activity in the real estate market has declined. (Uncountable)

"She can plan less activity" and "she can plan fewer activities" are equally correct and almost mean the same thing. "Activity" is a word that is often used both as a "countable" noun and an "uncountable" noun. That is why both "she is planning an activity" and "she is planning some activity" sound good. "Less activities", however, is something you should not say. Since "activities" is plural, it cannot be uncountable. It must be countable. You can have "two", "three", "more", "few", or "fewer" activities, but not "less". "Less" can only be used with uncountable things. The reason for this is usage, not grammar. We just don't use "less" that way even though we do use its opposite, "more", that way.