I have a question - will the head space change from the belt to the shoulder when resizing a 375 H&H round for second time if resizing the neck only? Is this dangerous? Thanks for the help.

belted mag, headspace on the belt .
Depends on how much you set the shoulder back on the first resize. if you set the sholder back several thousands the case will have to stertch to fill out the chamber and that could be a dangerous set of conditions. with the HH case I only shoot and resize a couple times.

If I do not move the shoulder and leave as formed would the head spacing then be governed by the shoulder vs the belt?

Necksizing should not effect cartridge headspace because you have not moved the shoulder back. It should rechamber easily. But be sure to measure case length after neck sizing before loading them.
When neck sized cases become difficult to chamber, the FL die will have to adjusted down so that it does push the shoulders back enough to allow the case to be rechambered w/o undue effort.If the shoulders are pushed back too far, that`s when problems arise.

If this gun is used for dangerous game or in any scenario where feed reliability is an issue, full-length sizing (for shoulder bump) is needed each time. If the shoulder is bumped too far, case stretch will result, shortening case life. The remedy is to have a gunsmith modify the chamber by trimming back the belt seat. Then the belt will be inconsequential in your reloading regimen.