Jughed your call. done thousands of miles over the last 25 years within 10 miles of the border without incident but they were all in california and before the current political climate.

i think you'll be fine. would be more worried about support like convenience stores, bike shops, cell service in case of mechanical/emergency/overt heat at that time of year.

first time in a few years not making it out to tucson at the beginning of the year. missing it already. quintessential, western americana.

frankly, twere i heading to tucson in may (may!!!!), first ride would be the entire enchilada of mount lemmon to the observatory tippy top and back 56 miles or so.

https://www.strava.com/activities/5121837109

you'll likely need arm warmers and a windbreaker 3/4 way up and probably for a spell down.
rest of your rides will (also) be sunrise-9:30am/10:00am before you become a fried egg sando.

do not know what you have ridden, or not, in previous visit(s).