This is entirely dependent on how your opponents view their poker investments. There are a few different ways your opponents think:
a) crushers think in terms of ev.
b) some others think in terms of their hand being worth $X.
c) some others only think about their hand and how often they'll flop something decent with no regard for the size of the investment.
So if you're at a table full of (b) players, you should loosen up significantly when there's a straddle; these players will think "oh I'd usually play this hand for $15 but I'm gonna fold for $30." All with no regard for the size of the investment relative to the existing pot nor your opening range. ATTACK!!!!!!!!
If you're at a table full of (c) players, you should tighten up the bottom of your opening ranges because they will call too often which will affect your winrate with the weaker hands that would otherwise be profitable at a table full of players with fold buttons.
If you're at a table full of (a) players, there are a few factors that will affect your ev with the marginal hands: first, the effective stack is cut in half relative to the blinds; what was a 100bb stack with normal blinds is a 50bb stack with a straddle; this seems to point us in the direction of tightening up. However, this isn't the only factor. The addition of the straddle changes everyone's ev at the table. What was a profitable position of being utg is now unprofitable for the straddler; nobody wins money in the blinds; everyone loses; thus the ev must be transferred to the other players. In order to capture this ev, there should be a loosening up effect for all of the other positions. Considering both of these effects isn't an easy task, but I think there should be generally looser play with a straddle than without. Here's a mind **** to illustrate why:
blinds are posted in a six handed game. Jimmy straddles utg 2bb. Joey restraddles in the hj to 4bb, Jane rerestraddles to 8bb in the co, I'm first to act on the button. Since everyone loses in the blinds, the ev loss from all the dead money in the pot is transferred to me on the button, thus I should play looser than I would vs standard blinds.
However, if given the option to rererestraddle to 16bb, I would do so.