Yes, you should, just maybe not today.
But once you have a bit of traction, and some market presence (say $1m in ARR?) … you might as well get to know your competitors.
You never know where will it go. You might merge the companies later, and Go Bigger Together. It might resolve some disputes between you. It might smooth any number of things over later.
It’s good to have cordial relations with your competitors, 90% of the time. Sometimes, though your whole ethos, your whole values, are about Killing The Competition. That can work. More here: Why You Should Kill Your Competitor in SaaS. There you sort of have to make them really the enemy, and any meetings will be viewed with skepticism by the team.
Even there. Maybe the CEOs should still quietly know each other.