I've been doing genealogy research lately, and when my great-grandparents immigrated to the US (around 1910), the only requirement for "legal" immigration was that they entered the country at a designated port of entry and were identified and documented on entry. Around 10 years later they were US citizens (and that length of time was more due to them not feeling they needed it, than due to any bureaucratic nonsense).
I expect that if we were to re-adopt a similar system today, it would not be catastrophic in the ways the government (both the left and right) would like us to believe. So I think you are branded anti-immigrant at times because being "anti illegal-immigration" is just kinda missing the point, and shows a lack of compassion and empathy for people who immigrate in ways that don't tick the arbitrary boxes.
The rules are not arbitrary. At least, they are only as arbitrary as literally every law is. You probably enforce similar rules in your own domain. Or maybe you are as compassionate and empathetic as you claim, and just let uninvited people stay on your property.
> and shows a lack of compassion and empathy for people who immigrate in ways that don't tick the arbitrary boxes.
It appears you have a savior complex. I'll guess you imagine illegal border crossers are all poor brown women with children fleeing gang violence, just yearning for freedom. Otherwise I'm not sure how you can talk about empathy and compassion about a group of millions of people per year who all have different experiences and motivations for illegally entering the US.