Why do businesses publicly take sides in politics? Wouldn't it make more sense to stay neutral?

Businesses that think its to their benefit to take sides will take sides.  Businesses that think its to their benefit to stay neutral will stay neutral.  Whatever decisions they make, may or may not work out like they intended.  

Whatever makes the business more money is usually the route they take. Planned Parenthood is a perfect example because they are in somewhat of a symbiotic relationship with the left since the right wants to end abortion. Another great example is the NRA (or ammunitions/weapons manufacturers) with the right since the left wants to have strict gun control.

Businesses, unions, and all non political organizations should stay neutral. Outlaw lobbying.  Unfortunately libs  demand that these groups side with them or they will call for bans, protests, and boycotts.  Libs’ use of coercion is common in communist countries to force others to do as they want.  

For control and profit.

To a true patriot it would make more sense.

Right wingers have been brainwashed by large corporations. They actually believe the rich should run the country rather than we the people.  The conservative cult has become anti American .

It depends on your target market. Some products are popular with one side of the political spectrum.

Most of them do actually give $$$ to both sides. Kinda like hedging your bets.