Evangelicals also get evangelised by other groups, and each other. Certain Christians always seem to be interested in trying to convince you you need a second baptism, or to get slain in the spirit, or that your understanding of the end times is backwards; that you should be attending certain seminars, reading such-and-such a book, or listening to some new preacher.
I often find it irritating, depending on the social skills of the presenter, so I well understand what non-Christians feel when Christianity in general is presented to them that way. Yet I don't feel insulted. I just think they're wrong, or majoring in minors. I don't think I have ever felt insulted by any such folks, including heterodox groups such as LDS or Jehovah's Witnesses. I didn't feel insulted by Christians witnessing to me before I became one myself. I can't imagine why I would. Just irritated. Uncomfortable. Buddhists, New Agers, and TM devotees don't evangelise by saying "you should convert to Buddhism," but by telling you practices you should adopt, or attitudes you should cultivate, or cool people they've run across who they think you should emulate because of the wonderful peacefulness/groundedness/tolerance they display. That's evangelism, and perhaps a bit more irritating because it isn't honest with itself about what is happening.
I find it irritating when wrong things get said (which explains my desire to challenge such things and return conversations to level ground). I understand the irritated response from those who disagree.
But if you are insulted, I think that's your own problem, not ours. Whether you learned it at your mother's knee or developed it as an adult, the idea that some great moral transgression has occurred if someone expresses that your religion is not adequate to eternal tasks, does not flow from Natural Law. Social transgression, sure. We evangelicals often take that risk and pay that social price. But equating that with moral transgression - you'll have to deal with that yourself, I think. Can't help you there.
There is also an interesting disconnect between uses of "convert" which causes much mischief. If I try to persuade some Hindu (or, heck, Christian from another denomination) to switch to my Covenant church, I do not say, or think, "I want to convert that person." I want them to be converted by something that they do to themselves, not something I do to them. The change in verb form indicates an important reality. Not even at a deeper level do I want God to "convert" them. God doesn't work that way. It's not an external force being applied to you.
In a nonreligious sense we say "convert miles to kilometers," and that very much carries the sense of an outside force being imposed on the numbers. To claim that evangelising is the same thing is just inaccurate. In fact, it is suspiciously inaccurate, as if the person needs to pretend that something is being done to them - that others are trying to make them do something. There were eras when new rulers took over and made everyone under their authority convert to some new religion. At a milder but still very wrong level, some countries have religious tests that one cannot hold certain jobs unless one belongs to the national religion. Those pressures do not obtain here.
So I give a suspicious glance when folks claim You/they are trying to convert me. I think it's an evasion, one more way to resist hearing what is said.
Irritating? Yes. We evangelicals raise our hand like a basketball player acknowledging a foul. We do that. Sometimes we don't like it any better than the recipient, because it can be socially uncomfortable for us, too. We try to find ways to get out of it, actually. But the complaint that we are insulting or trying to make someone do something? We don't own that. I think those come from inside the hearers.