As Rover says, it's not necessarily rude to say "I don't agree." It depends on how you use it. Tone matters. So does what else you say.
But if you want to soften it, there are countless ways to do it. Examples:
- Yes, up to a point. But ...
- That's certainly one way to look at it, but ...
- I understand. But have you considered ...?
- I'm glad you brought that up. The way I see it, ...
- Lots of people would agree with you. You might also look at it this way ...
- I appreciate that. On the other hand ...
- Before you make up your mind about that, you might keep in mind that ...
- Sure. I'm not surprised you feel that way. But think about this: ...
- Hm. I'm not entirely convinced. For one thing ...
- Okay. But then how do you explain ...?
- Maybe. But did you know that ...?
- Good point. I guess I'm more concerned that ...
There are also painfully trendy expressions:
- Let me push back on that a little.
- I honor your wisdom.
- Let's walk that back.
And, of course, there are ways that are, without exception, rude:
- What? Are you out of your mind?
- Ha! That'll be the day!
- Oh, yeah? Says who?
- Bollocks!
- What a bunch of bull!