Nah it's fine . Use a clear gel and my shirts are still good for months ... and that's gym shirts.
Use deodorant if you want but smearing scent on stink doesn't do shit for me. You still sweat and it still smells
I grew up and lived in AZ for most of my life. I haven't had A/C in my car for 3 summers. For years I used antiperspirant. I learned they were the reason I'd get white and yellow pit stains, so I switched to just deodorant (same brand). While I did technically sweat more, I didn't notice a different in smell. You're still going to smell after a long day, after all, regardless of how strong a deodorant/antiperspirant is. When I initially switched my pits itched a lot and eventually stopped with just deodorant. I didn't realize how often my pits were irritated from using antiperspirant.
Everyone's different, but it is pretty clear cut that antiperspirant is lessening the life of your shirts. Then again, most people go through their clothes faster than me. I have shirts old enough to drive, but they don't have pit stains.
Also, sweating is important for body-temp regulation and to block that up just means you're probably running hotter and you're sweating disproportionately more elsewhere (ie taking longer to cool down and thus sweating more overall, but not in your pits). I ain't a sweat scientist, but that's my thought on that.
edit: Also gel sticks are horrible in my opinion, like putting slime in there. I use AXE deodorant sticks - they used to be white/dry, but now they are more of a gel-like color, but aren't like the sticks I've used in the past that oozed out of slots and you smeared on.