Your question implies belief in magical forces that apparently aren't a proof of some other religion, or set of beliefs. If, indeed, one subscribes to such beliefs, then any story of miracles ought not present a problem, as even if true, they could be the result of such magic.[i]
Significantly, Rambam writes emphatically (Hilkhot Yesodei HaTorah 8:1) that belief in Judaism is not based on miracles, (but on the Sinaic revelation which the entire nation experienced), for miracles can be dismissed as magic or the like.
Accordingly, miracles occurring to members of other religions shouldn't pose a theological problem.
Indeed, the Torah itself (Deut. 13:2-6) describes a false prophet who promotes avoda zara, and performs miracles. Although this is probably referring to a Jewish "prophet", the message seems to be clear; miracles are not proof of legitimacy.
Regarding whether the miracles could be miracles, or must assumed to be fake, Midrash Tannaim (Deut. 13:3) records a dispute between R. Yossi the Galilean, and R. Akiva. R. Yossi suggests that the aforementioned false prophet could do an actual miracle, like stopping the sun. R. Akiva, however, considers it inconceivable that God would perform a miracle for a sinner. (Therefore R. Akiva suggests that the verse refers to a lapsed prophet who previously performed miracles when he was righteous).
It seems that according to R. Akiva, miracles performed by sinners (which doesn't necessarily include non-Jews) should be assumed to not be real, while according to R. Yossi, it could be an actual miracle.
However, even in light of R. Yossi's view, demonstrable miracles are few and far in between (cf. James Randi's million dollar challenge), so it is probably safe to assume that no miracle has taken place absent compelling proof to the contrary.
This Tannatic dispute also appears in Sifrei (Re'eh 84) and Sanhedrin (90a).
[i] Not that the existence of magic necessarily has to be accepted at all. See here regarding different approaches to the witch of En-Dor, and magic in general.