Looking for a 1911 sight pusher tool that removes the front and rear sights,
preferably one that doesn’t break the bank.

I bought one on Amazon a while back.  I believe it's made by NCStar.  Was about $50.  

Kind of a pain to align everything, but it works fine for the 1 or 2 times a years I change sights.
https://www.amazon.com/gp/product/B01HU4NNDE/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1

JMT

How much are you looking to spend brother? There are several different price points... If you want to give me an idea of the level you are looking for, I can give you a pretty good run down for you. I just spent a bunch of time looking at tons of pushers before I purchased mine. Just be careful when purchasing some that the price looks to good and instead read the reviews, especially if you buy via Amazon, as reviews are good way to figure out what kind of quality you usually will get. But sometimes I am wrong. If you need any help finding one let me know. Good Luck Brother.

Look at Fisher Solutions Sight Pusher… I own it and have pushed SIG and HK sights so far…. 1911’s be Easy.   Very reasonably priced

H

My gen 4 Sight-Tool was $60 and is built like a tank, I did add the cheesy moleskin for finish protection.