Yeah some areas probably are good to have math background like game programming if you want to apply physics or 3d transformation maybe... Matrix multiplication for rotations, transformations, I guess even things like ray tracing or colour operations, lighting etc.
I remember writing an analogue clock UI on a Casio pb2000c and Sinclair zx spectrum which required me to know trigonometry sine tangent cosine etc way back when I was in school, sure.
But consider some other areas... Like when I did cryptography coding early in my career. Sounds like an area which would require math chops? Nope! Concepts like encryption, decryption, digital signature, hashing etc were easy to pick up and implement in real products without having the need to know the math behind the actual algorithms like factorisation and what not. Leave the hard stuff to the domain experts.
Also reminds me of when I first got my hands on a PC on my father's office desk, again back when I was in school. When I got a bit familiar with the MS-DOS batch file command syntax I went and wrote a "conversational AI" as I now like to call it rivaling Alexa. Lol. It was just a bunch of bat files written and stored in a directory added to the path with names like hello.bat what.bat who why where when how .bat etc.
The code was just a hierarchy of if then else which checked for specific parameters provided to the batch files and printed a few random responses from a stored list.
So you typed "what is your name" and it would print a reply "my name is compaq" after matching the parameters "is your name" passed to the what.bat file lol.
I guess this is why you see memes joking that AI is nothing but just a complex structure of if then else statements.
No math required at all. Logical, critical, analytical thinking, yes. Very much required to write good programs that solve real problems.
To address op query though, yes it is very much possible to get a very decent and not just semi decent programming job with a little effort.
1. Logic is a branch of mathematics.
2. In the software industry, a lot of what you describe is called scripting. Unless imbued with other talents, people who do scripting are typically paid less than "programmers", and scripters not considered "software developers". In devops, sysadmin work, etc. one typically needs to do scripting but not programming.
3. In fact, the concept of "if" needs to come from algebra - a branch of mathematics. Plenty of people who don't understand algebra don't really understand "if". If you told them, "if graphics cards get cheap tomorrow, I'll buy this", they could answer "graphics cards won't get cheap tomorrow". Which is acceptable outside of algebra.
In algebra, same as in programming, it is not acceptable. In algebra, "if x = 3, what is 2x + 4?" cannot be answered "x can never be three, that will convert box into bo3".
4. It is sad that this assembling of other people's programs with scripts is being considered programming. Quality of software developers is going down, and good ones are very expensive. When no framework is available for a niche problem, such people are in trouble, googling whole day.
5. Yes, in cryptography, it is best not to meddle with the maths of it. Bruce Schneir once said that there are around 10 people in the whole world who are qualified to write a new cryptographic algorithm. But, I deal with people, who due to not understanding the basics, don't know when to encrypt, one way hash, sign, or encode. They also use these terms interchangeably, which confuses educated people.
On the same topic, generating unique numbers, vs various types of cryptographically secure random numbers is what many programmers need to do. Even scripters need to know the difference between /dev/random and /dev/urandom. Knowing which one you need, choosing between the alternatives, and using it needs some maths.
All in all, TL;DR, yes one can dodge all the situations where one needs maths and continue one's career of software development. One of my family members doesn't know how to turn a car on an upslope - they do drive. But still it is advisable to learn turning a car on an upslope when driving, and related parts of maths when starting a programming career.