I didn’t realize that was considered offensive as I’ve seen supporters of Trump refer to themselves that way. But if you’re looking for something, fire away!
I think that ever since 9/11 and the crazy conspiracies about bombs having been planted ahead of time, or that the burning jet fuel melted the steel beams, the reaction was a new coined term of "truther" that was applied to adherents of those conspiracy theories -- people who claimed to know the "truth" of what really happened.
In 2008, the "truther" term was converted into "birther" to attack people who questioned the authenticity of Barack Obama's on-line birth certificate.
Ever since then, the suffix "-er" as applied to any noun is used as an ad hominem to attack or discredit someone's support or beliefs. That's why using a term like "Trumper" can be seen as having its roots in the birther/truther movement, and is therefore seen by some as a personal attack.
Others might use it as a shortcut to represent a general area of support, but personally I abhor "thought" shortcuts because it leaves things open for interpretation.
-PJ