I decided to post my answer on PSE because I think it's already been unanswered for a long time here :)
Please keep in mind that I'm not really good at explaining (same reason as why I'm not trying to be active here), but I'll try my best. Also, please tell me if we can resize the spoiler box.
Take a look into the R on row/column 12/2. Let it not connected with the R on 12/3. As a consequence, the cell on 13/1 should be connected with R on 12/3. However, it'll break the rules. So, the RR should be connected. They should be connected through 12/3-12/2-12/1-13/1, else the H on 9/2 will have nowhere to go. Similar logic applied with B on 3/2 as well.
Take a look into A on 6/2. It'll have no another alphabet connected with it, or else some of column 1 cell will left empty. Also, you had no choice but make 5/1, 5/2, 6/1, and 6/2 as tetromino. Do some trivial stuff after this, and you'll have something like this.
Take a look into 10/3. A should have no connected character, else 9/3 will empty or there will be a contradict on neighboring on A-AX or D-DX. After that, it'll easily conclude on how 11/4 works by contradicting the rules on 12/7 for some pattern. So, it'll be like this.
Now everything is trickier than ever. If you take a look into 6/3, you know it should not be connected with H on 5/5. Our final choice is it's either connected with B on 4/4 or D on 8/4. However, if you connect it with the B, you'll have single empty cell on some upper cell which we should avoid. So, it must be D. Then, allowing similar logic with the AA on 6/2 and 8/2, we can do similar thing with BB on 6/2 and 2/8, which lead us into this.
Take a look into B on 2/8. it have no choice but make L shaped, else some upper cell will be empty. The I on 2/13 also should be on square shaped, else it'll neighboring with I on 4/12. But we don't know yet if it should fill the lefty or righty one. So, I'll leave it for now. Now let's go back to down side. Take a look at T on 12/12. If you decided to connect it up, it'll give some empty cell on the last column, and we don't want that. Applying this, we'll have some great break.
We want to fill the 10/12, but we have two possibility. It's either connected with H on 9/10 or A on 8/11. Let it connected with H, then you'll have some trouble with filling the centre part because the AB will be a neighbor. So, H should be stretch to left and let A fill the 10/12 and make it like this.
Applying green grasses rules on 8/9 (really hard to spot this one, but satisfying after I found it), we will have
Then just some nice filling with the squared I I mentioned above, it should be 'righty', or some cell on mid-left can't be divided as tetromino.
Thanks for the puzzle! :)