BIP148 and BIP149 are virtually identical except that BIP149 activates 6-12 months later in order to reduce turbulence. Distinguishing BIP148 as a "UASF" and BIP149 as "timed" is misleading: they're both UASFs, and both timed with the possibility of early activation in case of miner cooperation.
There are many very different "Segwit2x" proposals, but BIP91 is absolutely not one of them. It doesn't involve any max block size increase except for SegWit. BIP91 is a way of activating the original BIP141/BIP9 deployment at an 80% mining threshold rather than the original 95% threshold.
There is no single "Segwit2x" proposal that you can clearly point to.
OP tweaked again to rectify. I think the latest plan to activate SegWit2x is to utilise the signalling bits from BIP91, which is where I got mixed up.
This makes SegWit2x largely incompatible with BIP141, and especially with BIP148: Different nodes would be looking at different activation bits, meaning they could activate SegWit under different circumstances and at different times; and that would mess up SegWit-specific block relay policy between nodes, potentially fracturing the network.
BIP91
Now, it seems BIP91 has provided the solution.
BIP91 is a proposal by Bitmain Warranty (not to be confused with Bitmain) engineer James Hilliard which was specifically designed to prevent a coin-split by making SegWit2x and BIP148 compatible.
The proposal resembles BIP148 to some extent. Upon activation of BIP91, all BIP91 nodes will reject any blocks that do not signal support for SegWit through bit 1. As such, if a majority of miners (by hash power) run BIP91, the longest valid Bitcoin chain will consist of SegWit-signaling blocks only, and all regular BIP141 SegWit nodes will activate the protocol upgrade.
Where BIP91 differs from BIP148 is that it doesn’t have a set activation date, but is instead triggered by hash power. BIP91 nodes will reject any non-SegWit signalling blocks if, and only if, 80 percent of blocks first indicate within two days that’s what they’ll do.
This indication is done with bit 4. As such, the Silbert Accord can technically be upheld — 80 percent hash power activation with bit 4 — while at the same time activating the existing SegWit proposal. And if this is done before August 1st, it’s also compatible with BIP148, since BIP148 nodes would reject non-bit 1 blocks just the same.
This proposal gives miners a little over six weeks to avoid a coin-split, under their own agreed-upon terms. With a SegWit2x launch date planned for July 21st, that should not be a problem… assuming that the miners actually follow through.
So obviously miners are jumping on board with this.
//EDIT: -ck sums it up more succinctly in this thread.
//DOUBLE EDIT: Look at the last 1000 blocks. This looks like a pretty momentous shift.