Is declining a takeback request rude?

The 2 years I've been here, I almost always allow tackbacks in Casual games, but never in Rated games. I'm Way, way past a chess players prime, probably older than 90 % of the players here. So also slower than most, and probably behind on time in 90% of the Rapid or Classical games I play. I figure if a player is trying to play twice as fast as me, it's on them for not using that time for blunder checks and for "finger slip" checks. I sure as hec have to do it. In particular, if a player is clearly trying to rush me and get me rattled, as so often happens, but then THEY are the one that blunders.......them then turning around and asking me to think about granting a takeback while my clock is winding down, I find it rude in the extreme.

In any case, 2 weeks ago I read about the 'user preferences' option to eliminate tackbacks in rated games, and
I set mine to block them, so I presume problem solved.

I think when people decline it, they just are happy about the position and want to use your mistake

My position in short on takebacks:

Blunders - no
Mouseslips - yes, except in lightning or time scrambles
Opening mixups (thinking of atomic here) - yes, provided I trust the opponent

@JasonNewst How do you distinguish between a blunder and a mouseslip, the line between them is often very thin.

Grant yourself infinite takebacks: enable move confirmation in your profile.

I started by approving all takeback requests. I'm never going to be a pro, I play for fun, and there is something very satisfying about winning after allowing a takeback. But then I noticed that virtually nobody said thank you. And never offered to draw at the end of the game. The one time I requested a takeback, on my final move before winning, I thanked the opponent again and offered to draw the game since I was only winning due to his courtesy. Anyway, now I don't accept takebacks. I think any misclick I would, but I see virtually no misclicks, or I'm missing them.

Ill usually allow 1 per game

I don't want to pull myself into a losing position due to my hand accidentally moving a piece on the screen while it is trying to reach another part of the board...

No it's not. Turn off takeback requests from the settings.

Playing hastily and asking for a takeback is infamous.