In other workplaces, this may not be showing up as a trend yet. However, in academia (at least in the US) it is becoming more common because it is more common among students. My institution now allows students to specify their preferred pronouns, and passes that information along to instructors with each class roster (along with preferred call name, if that is not the same as the legal name). Students also will sometimes include this information in their email signature, as a low-stress way to convey this information. I have students with non-obvious preferred pronouns, and appreciate having this information ahead of time.
In this context, it can be seen as polite to reciprocate with one's own pronouns, even if they match one's apparent gender. University faculty and staff who regularly communicate with students who include this information in their signature may naturally begin to include the information, as well. Early adopters may do so specifically to help normalize the practice, and later adopters may do so because the practice is already normalized in their milieu.
If you do not ordinarily work with many trans folks, and this is not really the norm at your institution (i.e., you see it in only a small fraction of your email correspondence), then it's highly unlikely that there would be any negative consequences for omitting it from your email. I can even imagine that there could be some negative consequences for including it, if it comes across as un-genuine or if you're mainly communicating with a more conservative audience.
On the other hand, if you do regularly work with trans folks, and especially if you're in a supportive role to many trans students, you might want to consider whether you want to adopt the practice, even if it isn't yet a widespread practice.
And finally, if there genuinely is a wider trend at your institution towards including this information in all email signatures, then you may want to reflect on why you don't want to, and what messages the lack of information may send about you. If it's truly a standard component of email signatures for folks in your institution, then leaving it out would be a bit like leaving out your office phone number or title: many people wouldn't even notice, but anyone who needed that information and expected to find it there would probably wonder why it was omitted. This is fine if there's a good reason to leave it out, but maybe more friction than its worth otherwise.