Stock splits increase shares outstanding and share repurchase progams reduce shares outstanding. If a company has a stock split and then later repurchases shares are the two taken together at the least counter-intuitive?
No, I think you are misunderstanding the Math. Stock splits are a way to control relatively where the price per share can be for a company as companies can split or reverse split shares which would be similar to taking dimes and giving 2 nickels for each dime, each is 10 cents but the number of coins has varied. This doesn't create any additional value since it is still 10 cents whether it is 1 dime or 2 nickels.
Share repurchase programs though are done to prevent dilution as executives and those with incentive-stock options may get shares in the company that increase the number of outstanding shares that would be something to note.
Companies do both quite often. They have opposite effects on the share price, but not on the total value to the shareholders. Doing both causes value to shareholders to rise (ie, any un-bought back shares now own a larger percentage of the company and are worth more) and drops the per-share price (so it is easier to buy a share of the stock). To some that's irrelevant, but some might want a share of an otherwise-expensive stock without paying $700 for it.
As a specific example of this, Apple (APPL) split its stock in 2014 and also continued a significant buyback program:
This led to their stock in total being worth more, but costing substantially less per share.