It would really help if you stated where in the State you were looking to shoot?
I do NOT know of any gun clubs in the SE part of the state that put any restrictions on what kind of rifle you can use (IF they have a high power rifle range)!
Braintree R&P has a 50/100yd Rifle range (NO pistols allowed on this range) as well as 6 other ranges (including two state-of-the-art indoor ranges, jacketed pistol ammo allowed, no CF rifles indoors). They hold CMP shoots each month (except for Winter) where you are REQUIRED to use a military assault rifle

(M1, AR15, etc.). Lots of LEOs belong there. Safety rules are VERY strict and they have the best indoor range in the state.
www.brp.org I've been a member for 6+ years and highly recommend this place. If you want any further info, just ask.
Ames R&P (in North Easton) has a 50/100 yd and a 200/300 yd range. They also run monthly CMP shoots with M1s and AR15s. Club is "OK" but BOD keeps changing the rules on what you can/can't do on a regular basis and without any input from members. I've been a member here for 4-5 years and each year I contemplate dropping out rather than renewing.
http://www.amesriflepistolclub.net/
More clubs and specific info can be found at
http://www.goal.org/Clubs/affiliatedclubs.html, but if they aren't a GOAL affiliated club they won't be listed here (e.g. Ames R&P dropped out so they are no longer listed).