"Is tapering in whole mg amounts immunologically safer/as safe as tapering half mg amounts?"
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I personally don't think tapering by half mg amounts is necessary. I tried that too and it didn't make any difference. I agree with @jeff97 and just request the 2.5 mg and 1 mg tablets. Using those two tablets should allow you to do .5 mg increments except for 1.5 mg and .5 mg.

I have done it the way your rheumatolgist suggests too by doing 5 mg one day and 4 mg the next. Over 2 days, that averages 4.5 mg. That makes more sense to me if you want to prompt your adrenals to produce cortisol again. On the day you take the 4 mg dose that might give your adrenals a hint to make up the difference and produce some cortisol. I'm not sure if it works that way or not. I mostly say whatever works for you is all that matters.

I was flabbergasted when my endocrinolgist told me there was no need to taper from 3 mg to zero IF my cortisol level was adequate. It depended more on my cortisol level than my autoimmune disorders.

I think my endocrinologist consulted with my rheumatolgist to make sure I didn't need Prednisone to treat PMR. She also asked me I thought I needed Prednisone for PMR. I wasn't sure but Actemra seemed to have PMR under control.

Actemra wasn't intended to prevent uveitis from recurring. However, after some dose adjustments made easier with an infusion, of Actemra, it now seems like it can prevent flares of uveitis too.