Supposing I have applied the formatting to the range cells as following screenshot shows, and now I will talk about how to protect worksheet's formatting only step by step:

1. Select the range cells that you want others to be able to edit, and then right click and choose Format Cells from the context menu, see screenshot:

2. In the Format Cells dialog box, click Protection tab, and uncheck the Locked option. See screenshot:

3. Click OK to close the dialog box.

4. If you need to allow others to edit multiple ranges in this worksheet, please repeat above step 1-4 as you need.

5. Go on to click Review > Protect Sheet to protect the worksheet, see screenshot:

6. And in the popped out dialog box, make sure the Format cells is unchecked (it is not checked by default), and you needn't change any information in the dialog box, see screenshot:

7. Then click OK, and all the selected cells content can be edited as your need, but the cell formatting can't be modified.

Note: If you want to set a password to protect the sheet, you can enter the password as your need, but if you needn't, just only click OK button in the Protect Sheet dialog box.

If you have Kutools for Excel installed, you can simplify steps to protect current worksheet’s formatting only. Please do as follows:

1. Select multiple ranges that you will allow other to edit, and click the Kutools Plus > Worksheet Design to activate the Design tab, and then click the Unlock Cells button on the Design tab. See screenshot:
Note: Holding the Ctrl keys, you can select multiple non-adjacent ranges by selecting one by one.

Then a dialog box pops out and reminders you selected ranges have been unlocked. Just close it.

2. Click the Design > Protect Sheet or (Review > Protect Sheet) to protect current worksheet.

3. In the opening Protect Sheet dialog box, enter your password, and remember not to check the Format Cells option, and click the OK button. Next reenter your password in the Confirm Password dialog box, and click the OK button.

Quickly mass password protect multiple/all worksheets in Excel

Normally Excel's Protect Sheet feature can only protect active sheet. However, Kutools for Excel's Protect Worksheet utility enables to mass protect multiple (or all) worksheets with same password by only 2 steps.