Understanding the Strength vs. Flexibility Conundrum

I found a common concern that’s raised in martial arts circles regarding strength training and its effects on flexibility on a recent Reddit post.  Let’s read:

I’ve been struggling for years to find a balance between building muscle (especially legs) through weight training and improving flexibility. I feel like I’ve tried everything, or maybe i just wasn’t patient enough. I would train legs through weighted squats, then I’m so sore and tight (especially hamstrings) i cannot stretch probably for most of a week. So i would start to get bigger legs but then my flexibility and kicking would go down hill. Then i would freak out and back off weight training and focus on flexibility again but then my legs never seem to grow. I know it’s possible to do both within reason, are there others who have had similar experiences and if so how did you work around…