Not sure if you've ever been involved in a suit, but the "first sign of conflict" is a critical juncture. Perhaps the most critical. And, in many cases, your decision is a function of simple math.
Once you proceed past the "first sign of conflict", you will quickly sink a lot of cash. You don't get a refund if you later decide to stop, nor any other credit. That money is gone and either you keep going until you a.) win (or lose) a protracted, costly battle; b.) bankrupt your cash, energy, or will; or c.) find an opportunity to settle and stop the bleeding. By then, the damage is done.
So, if you decide to proceed, then you are signing up for significant cost and a ride for which you have limited control. They will keep throwing stuff at you to entangle and frustrate you. If you take the suit as far as discovery, then you can get into the high 6-figure or even 7-figure range before you know it.
And, before you get to discovery, the motions, counter-motions, and other pleadings can easily get you to six figures within a few short months or less (depending on the complexity of the case).
If you are a small business, it can be a non-starter, especially when the plaintiff is a much larger (and hostile) company. I've been through it personally and I decided not to "capitulate at the first sign of conflict". I was pissed, they were wrong, I wouldn't be bullied, etc. So, I fought it.
We handily beat them back on the initial injunction they were seeking. Based on the merit, we knew we'd win that easily. Still, it cost me ~$20K to actually do it. It doesn't matter how weak their case is. They can make you bleed to prove it. The standard for having the suit labeled frivolous is extraordinarily high and you almost assuredly will not recover your legal fees.
We kept fighting, using some of the foundation (research, etc.) laid during the injunction battle to reduce costs. Still, by the time, we reached the mandatory (in the state of CA) settlement conference (where we decided to settle), we were out over $100K. So, that was the price of "not capitulating at the first sign of conflict". Of course, we didn't have to concede everything they initially demanded, but that small victory felt a bit Pyrrhic.
And, none of this cost includes the time, mental energy, and stress involved. If you are running a small business, you likely don't have time/energy for it. So, beyond literally bankrupting you, it can damage your business (perhaps irreparably) in other ways.
My strategy, if I can't talk people out of their legal threats and requests for content removal, is to replace the content with something like "Content removed at the request of [fullname]." I figure that anyone likely to have taken warning from the original content having find it on Google will potentially get the same from that notice. e.g., if they're asking for stuff to be removed, maybe there's something going on.
Source: I've run a public forum with anonymous posting for about 10 years and get regular legal/removal threats. Had four in one day the other week. None have ever proceeded beyond a threatening letter from a lawyer and most don't get past "I've printed this out and I'm taking it to my lawyer."