Welcome to the forum, bro.
Rule #1 - The boss is always right.
And you know rule #2.
Your curiosity and initiative are admirable and will enhance your value to employers in the future. Keep that up! But I can tell you this - your boss does not want to hear "some guys on some forums said I should consider friction." Not a good career move. Feel free to run your calculations with and without, at whatever level you might want. If you can find a good reason to consider friction, bring it up to him, but don't base your suggestion on comments you read on line. Base it on your own research and calculations.
This is one of those early lessons engineers learn after school. You can calculate all you want, and you should, but when it comes to applying it in the real world (unless you're in something like aerospace), you're probably going to end up doubling everything. You'll learn that oversizing is generally less costly than unexpected failures.
You'll also learn that no matter what you do as an intern, they probably aren't going to implement any of it without a thorough review by one of the staff engineers.
You'll also learn that they WANT you to ask if you are unsure. If you can bring your research with you when you ask, that helps a lot.
Oh, and to your original question about whether or not to consider friction? That will depend on the conditions of the bearings and the contact surfaces, which is different in every plant. Do not forget that whatever conditions you see there now will change in the future. And when that cart stops because of some little crap on the track, they aren't going to blame the crap on the track. They're going to blame the "damned engineer" that undersized the drive.
So, the boss might be telling you to ignore friction, but he's also going to tell you to oversize the drive significantly. So, in his mind he is accounting for it, without spending time calculating it.
One more thing - my big congratulations and praise for not falling prey to the common and infuriating practice of so many in the young "texting" generation: that of thinking all written communication is the same as texting! Business writing should always exhibit proper grammar, spelling, capitalization, and punctuation. Thank you!