minimum required compaction degree for reinforced fill

You're opening a kettle of fish on this....

Are you talking dry density by modified or standard proctor?

geotextile or geogrid? I wouldnt really call fill reinforced if it had a layer of geotextile at the base. I would if it had a layer of geogrid.

Also, what degree of compaction seems to depend on your experience (based on what i have read on this forum and on other sources).

I was thought that a minimum would be 98%. We had that in our standard specification for structural filling. It was previously 95% for 10 plus years (since the spec was started) but then it was reviewed and changed to 98% by the powers to be at my company. Since then we specify 98%, regardless of if we have a geogrid/getextile or not.

If i had a 1m deep fill layer with a layer of geotextile at 0.8m depth, i think i would still be asking for 98%

Per the "Handbook of Geosynthetics", published by the Geosynthetic Material Association, use the same compaction that would be used without a geosynthetic. Note the caution about compaction of the first 12" of soil on the the fabric:

I am gonna be more precise.
This is an MSE wall about 8 m high composed of crushed tuffa excellent fill material , something you guys would classify as A-1-a. the contract specifies modified proctor references while i used to believe that a standard test would be enough especially since there will be no vehicles circulating above the wall when the project is delivered. Vibratory equipment is prohibited since the MSE function is to protect a small cliff harboring an archaeological site from falling .
I made the preliminary decision of accepting about 90% of the modified Proctor MDD.

Edit: iv'e checked out some pdf on the net and some of them recommand using 95% from the T-99 AASTHO for slopes and walls and 100% for walls supporting foundations

This has always been a controversial issue and varies on a regional level in the US. The fact that MSE is involved should not alter the density requirements as it tends to be a soil strength and consolidation issue related to the function(s) of the structure. What does the MSE structure support when done? Any displacement requirements? What is the maximum lift thickness going to be? and so on.

If there are minimal fines in the A-1-a backfill( <5% would be preferred if vibratory equip is not allowed), the differences will not be significant and just use 95% of whatever you want. I do not think anyone would endorse 90% if the fill is expected to behave. If there are fines then moisture and method will come into play. The ultimate method in my opinion is to run a standard and modified density series and compare densities and moisture contents. It is pretty easy to see how the material responds to extra effort and what the moisture content does.