No, but it’s complicated. There are two places the ® symbol appears: in the logo, and following the registered trademarks.
First, let’s talk about FIRST’s logos. These must be assumed to be copyrighted (by virtue of being artistic works that aren’t of obviously trivial complexity), so if you remove the ® symbol from the logo, you may be creating a derivative work against the terms of the licence (which specifies “FIRST and LEGO copyrighted materials may never be used in any modified form.”).
As for their trademarks and service marks, you can’t use those marks in a way that would dilute FIRST’s brand or mislead people—those are tenets of trademark law which apply irrespective of any licence. But you can use the trademarked names nominatively or in terms of the word “first” (e.g. “the first robotics competition”, meaning the inaugural one), and there’s little FIRST can do about it. For example, I’m not attaching ® to any instance of “FIRST”, nor am I italicizing it,* nor am I posting disclaimers. But they have no cause of action, because these uses are permitted under the law in order that people may comment upon the subject of the mark.
Here’s the confusing part: this freedom might not apply to you if you’re using their logo—because then you’re expected to assent to the terms of licence in order to use their copyrighted material, and those terms of licence impose restrictions on you. Some of those licence restrictions cover the logo itself, but there are additional restrictions that cover the trademarks too. (In theory, that licence is an agreement between you and FIRST.)
However, their licence is not the only way you can use the logo: for certain purposes, you can do so under the principle of copyright fair use, without any licence—so it’s actually entirely possible to avoid all restrictions that FIRST has placed in the licence. But to do this, you have to restrict yourself to legitimate fair use to avoid infringement.
Oftentimes, you’ll find that companies will aggressively assert intellectual property rights, in order to strengthen any future cases. They may be overplaying their hand, so as to demonstrate that they have actively engaged in the defence of their property (to overcome an argument of abandonment or genericization).
As a practical matter, nearly everything that is posted on ChiefDelphi in relation to FIRST’s intellectual property would fall under one of the exemptions. (Therefore compliance with the terms of licence in that context would usually be irrelevant.)
As a final complication, there’s one hypothetical way that FIRST could, if feeling particularly vindictive, strike back at people using their marks in legal ways that they didn’t appreciate. Since we’re all participants in the various FIRST programs, they could retaliate by making compliance with their logo guidelines a necessary aspect of participation. (Of course, this would be stupid, and wouldn’t endear them to anyone.)
Now, with all that said, those are your legal rights. You can always be nice to FIRST and do what they ask of you, even absent any formal requirement to comply. But in my case, at least, I find the italics to be an abuse of typography and won’t stand for them.
*Except where I quoted them—and that quote is an example of a fair use extract for the purposes of critical commentary.